There was plenty of endeavour but only sporadic moments of quality
Fulham remain without a win at Burnley since 1951 as a keenly contested game deservedly finished even at Turf Moor.
The visitors had two golden chances in the opening minutes but the first half was a largely forgettable affair.
Bobby Zamora collected a long free-kick from Chris Baird and held off Steven Caldwell to put Fulham ahead with a right-foot shot into the bottom corner.
But the home side rallied and Wade Elliott equalised with a fine volley into the roof of the net from 15 yards.
The omens for a Fulham victory were not good, their last success at Turf Moor coming when tea rationing was still in operation, and 28 matches had gone by without a win in the 58 years since then.
But Burnley had conceded 11 goals in their last four games, and the Cottagers, who had lost only once in nine, might have been two up inside the first two minutes.
Erik Nevland touched on Zamora's pass to put Damien Duff clear on the right-hand side of the area but the former Blackburn winger, whose every touch was roundly booed, shanked horribly wide trying to chip the giant Brian Jensen with his right foot.
Moments later, Nevland's low shot was blocked by Jensen with his legs.
At the other end Robbie Blake's 20-yard left-foot volley was parried by Mark Schwarzer but the best of the chances continued to fall to the visitors, and Duff cut in from the right to unleash a stinging drive with his more favoured left foot, forcing a smart save from Jensen to his left.
We should have won the match - Hodgson
Burnley winger Chris Eagles briefly gave the home contingent some encouragement with a mazy run and deflected shot that Schwarzer kept out, but the match descended into an extremely scrappy affair.
Later, Fulham felt Eagles was offside when he drifted through but play was allowed to continue and Schwarzer needed to make a fine save, although the remainder of the half was notable only for the lack of incident and fluency.
Burnley started the second half brightly and Andre Bikey played in Elliott, but he dragged his shot from the edge of the box badly wide.
David Nugent was introduced in an attempt to inject some firepower into the home attack but Fulham went ahead as Chris Baird's quick free-kick from inside the centre circle saw Zamora wriggle free from Caldwell's challenge, and his finish across the goalkeeper was clinical.
Coyle happy with 'valuable point'
However, 10 minutes later Elliott made amends with a superbly controlled shot into the top corner after Stephen Jordan's cross from the left flicked off the head of Fulham defender Aaron Hughes.
The home fans urged their side forward again but the next chance fell to the visitors as Zamora just failed to connect with Brede Hangeland's through ball, having appeared to have been dragged back by Caldwell.
In the end the decisive moment of inventiveness or fortune eluded both sides and neither could feel seriously aggrieved with a point.
Burnley manager Owen Coyle:
"I thought it was two teams going all out to win.
"Fulham were very impressive, as good as anything we have seen at Turf Moor this season.
"But coming back from a goal down showed a lot about our character.
"We know the quality in the Premier League and it's a learning curve for us but the players have an appetite for it and a quality and we play the right way."
Fulham boss Roy Hodgson:
"We were more than good value for a point.
"We created some excellent chances, especially in the first-half.
"It was a difficult place to come and if I'd been offered a point before the game I would have been tempted.
"But after the way we played in the first half I think I can be a little bit disappointed that we didn't take all three points."
90:00+2:29 Corner taken right-footed by Wade Elliott from the right by-line to the near post, clearance by Bobby Zamora.
90:00+0:34 Shot from just outside the box by Fernando Guerrero misses to the left of the goal.
85:09 Substitution (Burnley) makes a substitution, with Fernando Guerrero coming on for Chris Eagles.
83:46 Free kick awarded for a foul by John Pantsil on Chris Eagles. Chris Eagles crosses the ball from the free kick right-footed from left wing.
83:14 A cross is delivered by Wade Elliott, save by Mark Schwarzer.
81:54 Free kick awarded for a foul by Steven Fletcher on Aaron Hughes. Aaron Hughes takes the free kick.
81:34 Bobby Zamora takes a shot. Save by Brian Jensen.
79:24 Zoltan Gera has an effort at goal from outside the box missing to the wide left of the goal.
77:27 Stephen Jordan gives away a free kick for an unfair challenge on Damien Duff. Free kick crossed left-footed by Damien Duff, save made by Brian Jensen.
76:38 Substitution Kevin McDonald joins the action as a substitute, replacing Andre Bikey.
76:38 Substitution Zoltan Gera comes on in place of Erik Nevland.
75:09 Andre Bikey takes a shot. Save by Mark Schwarzer.
73:42 Shot by Erik Nevland from deep inside the penalty area misses to the right of the goal.
73:05 Free kick awarded for a foul by Stephen Jordan on Damien Duff. Free kick crossed by Aaron Hughes, clearance by Graham Alexander.
72:20 The referee blows for offside against David Nugent. Brede Hangeland restarts play with the free kick.
71:38 Tyrone Mears produces a cross, save made by Mark Schwarzer. Wade Elliott takes a shot. Blocked by Brede Hangeland.
69:47 Jonathan Greening takes the inswinging corner, save made by Brian Jensen.
68:57 Unfair challenge on Clarke Carlisle by Clinton Dempsey results in a free kick. Indirect free kick taken by Brian Jensen.
67:29 The official flags Bobby Zamora offside. Clarke Carlisle restarts play with the free kick.
66:27 Corner taken right-footed by Chris Eagles to the near post, Bobby Zamora makes a clearance.
64:35 David Nugent takes a shot. Save made by Mark Schwarzer.
63:08 Corner taken right-footed by Chris Eagles to the near post, Bobby Zamora manages to make a clearance.
Correction - 61:44 Shot by Clinton Dempsey. Corner taken by Jonathan Greening from the left by-line to the near post, Andre Bikey manages to make a clearance. Blocked by Clarke Carlisle.
61:44 Effort on goal by Clinton Dempsey from just inside the box goes harmlessly over the target. Corner taken by Jonathan Greening from the left by-line to the near post, Andre Bikey manages to make a clearance.
60:38 Jonathan Greening challenges Graham Alexander unfairly and gives away a free kick. Graham Alexander takes the direct free kick.
59:14 GOAL - Wade Elliott:Burnley 1 - 1 Fulham Wade Elliott gets on the score sheet with a goal from deep inside the penalty box to the top left corner of the goal. Burnley 1-1 Fulham.
59:08 Centre by Tyrone Mears,
58:53 The ball is sent over by Wade Elliott, clearance by Brede Hangeland.
55:51 Free kick taken by Brian Jensen.
55:51 Substitution Robbie Blake leaves the field to be replaced by David Nugent.
55:51 Damien Duff concedes a free kick for a foul on Clarke Carlisle.
54:45 Inswinging corner taken left-footed by Damien Duff from the right by-line, Clinton Dempsey takes a shot. Blocked by Clarke Carlisle.
54:31 A cross is delivered by Damien Duff, Clarke Carlisle makes a clearance.
53:49 Unfair challenge on Chris Baird by Steven Fletcher results in a free kick. Mark Schwarzer takes the indirect free kick.
49:50 Chris Baird provided the assist for the goal.
49:50 GOAL - Bobby Zamora:Burnley 0 - 1 Fulham Bobby Zamora finds the net with a goal from inside the penalty area to the bottom left corner of the goal. Burnley 0-1 Fulham.
49:43 Steven Fletcher gives away a free kick for an unfair challenge on Brede Hangeland. Chris Baird restarts play with the free kick.
49:09 Shot by Wade Elliott from deep inside the penalty area misses to the left of the target.
47:17 Damien Duff delivers the ball, clearance by Clarke Carlisle.
46:32 The ball is crossed by Wade Elliott.
45:42 Steven Fletcher fouled by Brede Hangeland, the ref awards a free kick. Robbie Blake delivers the ball from the free kick right-footed from right channel, clearance by Brede Hangeland.
45:01 The second half begins.
Half Time
45:00+1:28 The referee calls an end to the first half.
43:31 Steven Caldwell concedes a free kick for a foul on Bobby Zamora. Damien Duff crosses the ball from the free kick left-footed from right channel, clearance by Graham Alexander.
40:15 Chris Eagles has an effort at goal from 25 yards. Save made by Mark Schwarzer.
39:33 Andre Bikey challenges Bobby Zamora unfairly and gives away a free kick. Free kick taken by Chris Baird.
39:00 Foul by Bobby Zamora on Graham Alexander, free kick awarded. Brian Jensen takes the direct free kick.
38:30 Booking The referee shows Paul Konchesky a yellow card.
37:33 Chris Eagles takes a shot. Mark Schwarzer makes a save.
35:03 Booking Jonathan Greening receives a caution for unsporting behaviour.
34:54 Unfair challenge on Andre Bikey by Jonathan Greening results in a free kick. Free kick taken by Brian Jensen.
34:44 Damien Duff delivers the ball, Steven Caldwell manages to make a clearance.
29:48 Bobby Zamora fouled by Steven Caldwell, the ref awards a free kick. The free kick is delivered right-footed by Jonathan Greening from right channel, Wade Elliott makes a clearance.
27:36 Stephen Jordan gives away a free kick for an unfair challenge on Damien Duff. Aaron Hughes takes the free kick.
25:47 Chris Eagles crosses the ball, Aaron Hughes makes a clearance.
24:07 Robbie Blake crosses the ball, Mark Schwarzer makes a save.
23:28 Robbie Blake takes the outswinging corner, Brede Hangeland makes a clearance.
22:49 Centre by John Pantsil, Chris Baird takes a shot. Save made by Brian Jensen.
21:48 Free kick awarded for a foul by Clarke Carlisle on Erik Nevland. Free kick taken by Clinton Dempsey.
21:27 Free kick awarded for a foul by Stephen Jordan on Damien Duff. Free kick taken by Aaron Hughes.
20:01 The referee gives a free kick against Paul Konchesky for handball. The free kick is delivered right-footed by Graham Alexander from right wing, Damien Duff makes a clearance.
18:48 Unfair challenge on Chris Eagles by Clinton Dempsey results in a free kick. Graham Alexander takes the free kick.
17:01 Effort on goal by Clinton Dempsey from outside the box goes harmlessly over the bar.
16:17 Outswinging corner taken by Robbie Blake from the right by-line, clearance by Clinton Dempsey.
14:48 Tyrone Mears crosses the ball, clearance by Paul Konchesky. Robbie Blake delivers a pass corner to short.
13:07 Chris Eagles takes a shot. Mark Schwarzer makes a save.
11:46 John Pantsil delivers the ball, clearance by Tyrone Mears. Effort on goal by Chris Baird from just inside the penalty area goes over the target.
10:26 The ball is delivered by Damien Duff, clearance by Tyrone Mears.
9:06 Damien Duff takes a shot. Save made by Brian Jensen.
7:06 Effort on goal by Robbie Blake from 25 yards. Save by Mark Schwarzer.
6:15 Free kick awarded for a foul by Steven Fletcher on Jonathan Greening. Direct free kick taken by Aaron Hughes.
6:00 Paul Konchesky crosses the ball, Brian Jensen makes a save.
4:24 The ball is crossed by Stephen Jordan, Jonathan Greening makes a clearance. Corner taken right-footed by Robbie Blake, clearance made by John Pantsil.
1:53 Erik Nevland takes a shot. Save made by Brian Jensen. Inswinging corner taken left-footed by Damien Duff from the right by-line, save by Brian Jensen.
0:56 Damien Duff produces a right-footed shot from just outside the box that misses to the right of the goal.
0:00 The ref blows the whistle to begin the match.
Live text and data provided by The Press Association.
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