West Ham were also unimpressive but boss Gianfranco Zola, who was "completely shocked" by crowd trouble during the midweek game against Millwall, will have been cheered by his team's spirited display.
Manager Zola is short of options in attack and was unable to complete the signing of striker Alessandro Diamanti from Italian side Livorno in time for him to be included in the Hammers squad.
That meant Cole operated as a lone frontman, with on-loan Inter Milan midfielder Luis Jimenez pushing forward to support him.
Allardyce pleased to get first point
Cole did unsettle the Rovers defence at times and created the best chance of the first half.
The former Chelsea man collected Scott Parker's pass and sneaked between Lars Jacobsen and Vince Grella before out-sprinting Chris Samba and firing high and wide from an awkward angle.
The home side struggled to get going and new signing Pacsal Chimbonda, making his Blackburn debut, twice had to move across from left-back to superbly tackle Jiminez as he was about to shoot.
Blackburn's best opening of the first half came when Samba headed Dunn's free-kick towards Jason Roberts, who stretched to poke the ball into the side netting.
Rovers themselves lacked a cutting edge up front and missed Benni McCarthy, who sat out the game because of an ankle problem.
Blackburn manager Sam Allardyce introduced Canadian-born forward Hoilett - known as Junior rather than David - on the hour-mark.
Zola promises better form to come
The 19-year-old had an opportunity to open the scoring but shot wide of the near post from the edge of the six-yard box after latching onto Dunn's pass.
Hoilett then returned the compliment by picking out Dunn, whose tame shot was comfortably held by Green.
That prompted Allardyce to send on £6m summer signing Nikola Kalinic for his home debut.
The lanky Croatian striker offered Rovers an aerial option, but their best chance in the closing stages came when Dunn again set up Hoilett - this time on the break following a West Ham attack.
Dunn looked up and found Hoilett with a fine pass with the outside of his right foot and the youngster did well to lift the ball over Green, but also lifted it over the bar.
Blackburn's Morten Gamst Pedersen tried his luck with a late free-kick, which also went over.
• Blackburn manager Sam Allardyce: "We're building well, but the results are not reflecting that.
"We're creating chances but not taking them. At least we have got the defensive side sorted and we got stronger as the game went on and could have won it.
"We played the way we did because of the players we had available - and we played it very well. All you punters and supporters out there, leave it to me. I'm the expert, not you."
• West Ham manager Gianfranco Zola: "It was difficult because this was our third game in six days and the other day against Millwall we played for 120 minutes, and it was a very exhausting game.
"We found that in the second half our performance dropped a bit, but we defended well and deserved a draw, and I'm happy with that.
"In the first half we played quite well and Carlton Cole had a clear chance for us. But in the second half they also had a clear chance, so it's a good point for us."
90:00+4:16 The final whistle goes and the game is over.
90:00+3:24 Inswinging corner taken by Morten Gamst Pedersen, free kick awarded for an unfair challenge on Robert Green by Christopher Samba. Robert Green takes the direct free kick.
90:00+3:10 Christopher Samba takes a shot. Blocked by Matthew Upson.
90:00+2:34 Radoslav Kovac gives away a free kick for an unfair challenge on Vincenzo Grella. Paul Robinson restarts play with the free kick.
89:25 Christopher Samba produces a cross, clearance by James Collins.
87:38 Effort from inside the area by David Hoilett misses to the right of the goal.
86:26 Substitution Radoslav Kovac comes on in place of Jack Collison.
85:18 David Dunn takes the chance to get an effort at goal. Robert Green makes a comfortable save.
84:24 Carlton Cole challenges Vincenzo Grella unfairly and gives away a free kick. Direct free kick taken by Keith Andrews.
83:40 Shot from just outside the box by Junior Stanislas goes over the bar.
82:39 Corner taken left-footed by Morten Gamst Pedersen, Carlton Cole makes a clearance.
Correction - 82:08 David Hoilett takes a shot. James Collins gets a block in.
82:08 David Hoilett takes a shot. Blocked by James Collins.
80:02 Vincenzo Grella fouled by Carlton Cole, the ref awards a free kick. Paul Robinson takes the direct free kick.
78:49 Shot comes in from Morten Gamst Pedersen from the free kick.
78:49 Booking The referee shows Scott Parker a yellow card for unsporting behaviour.
77:45 Matthew Upson gives away a free kick for an unfair challenge on David Dunn.
76:51 David Hoilett produces a right-footed shot from just outside the penalty area that goes harmlessly over the target.
76:11 Scott Parker fouled by Morten Gamst Pedersen, the ref awards a free kick. Mark Noble takes the direct free kick.
75:08 The referee blows for offside. Paul Robinson restarts play with the free kick.
74:04 Direct free kick taken by James Collins.
74:04 Substitution Nicola Kalinic replaces Jason Roberts.
74:04 Booking The referee cautions David Dunn for unsporting behaviour.
73:53 Free kick awarded for a foul by David Dunn on Kieron Dyer.
71:19 David Dunn takes a shot. Save by Robert Green.
69:43 Shot from just outside the box by David Dunn misses to the left of the goal.
69:03 Carlton Cole gives away a free kick for an unfair challenge on Pascal Chimbonda. Paul Robinson restarts play with the free kick.
68:37 Free kick awarded for an unfair challenge on James Collins by Christopher Samba. Direct free kick taken by Robert Green.
68:27 Unfair challenge on Pascal Chimbonda by Carlton Cole results in a free kick. Direct free kick taken by Paul Robinson.
67:15 David Hoilett has an effort at goal from deep inside the area missing to the left of the target.
65:42 Free kick taken by Paul Robinson.
65:42 Substitution Luis Jimenez leaves the field to be replaced by Kieron Dyer.
65:42 Jack Collison challenges Pascal Chimbonda unfairly and gives away a free kick.
65:00 Corner from the right by-line taken by David Dunn, Christopher Samba takes a shot. Robert Green makes a save.
64:20 Free kick awarded for an unfair challenge on Vincenzo Grella by Luis Jimenez. Gael Givet takes the direct free kick.
63:06 Jason Roberts challenges James Collins unfairly and gives away a free kick. Robert Green restarts play with the free kick.
60:43 Shot by Scott Parker from outside the box goes over the net.
59:32 Robert Green takes the free kick.
59:32 Substitution David Hoilett joins the action as a substitute, replacing Steven Nzonzi.
59:32 Jason Roberts challenges Jonathan Spector unfairly and gives away a free kick.
57:07 Shot from just outside the area by Morten Gamst Pedersen misses to the left of the target.
Correction - 56:07 Junior Stanislas takes a shot. Christopher Samba gets a block in.
56:07 Junior Stanislas takes a shot. Blocked by Christopher Samba.
53:43 The ball is swung over by Morten Gamst Pedersen, Christopher Samba takes a shot. Save by Robert Green.
53:43 Booking Mark Noble receives a yellow card.
53:38 Foul by Mark Noble on David Dunn, free kick awarded.
53:14 Christopher Samba concedes a free kick for a foul on Scott Parker. Free kick taken by Robert Green.
52:49 Jonathan Spector concedes a free kick for a foul on Steven Nzonzi. Paul Robinson restarts play with the free kick.
51:51 David Dunn is ruled offside. Free kick taken by Robert Green.
49:51 Julien Faubert concedes a free kick for a foul on David Dunn. Free kick crossed by David Dunn, Robert Green makes a comfortable save.
49:05 Inswinging corner taken from the right by-line by Mark Noble, Shot from inside the area by James Collins clears the bar.
48:24 Steven Nzonzi gives away a free kick for an unfair challenge on Mark Noble. Direct free kick taken by Robert Green.
47:43 Effort on goal by Carlton Cole from outside the box goes harmlessly over the bar.
47:07 The official flags Morten Gamst Pedersen offside. Indirect free kick taken by Robert Green.
45:01 The referee starts the second half.
Half Time
45:00+2:20 It is the end of the first-half.
44:12 Effort on goal by Steven Nzonzi from outside the area goes harmlessly over the bar.
41:47 Junior Stanislas crosses the ball.
40:05 Pascal Chimbonda takes a shot. Comfortable save by Robert Green.
39:24 Unfair challenge on Scott Parker by Jason Roberts results in a free kick. Direct free kick taken by Scott Parker.
37:31 Keith Andrews takes a shot. James Collins gets a block in.
29:55 Carlton Cole gives away a free kick for an unfair challenge on Gael Givet. Free kick taken by Gael Givet.
28:49 Free kick awarded for an unfair challenge on Vincenzo Grella by Scott Parker. Direct free kick taken by Paul Robinson.
26:59 Corner taken by Morten Gamst Pedersen, Keith Andrews produces a header from inside the area that goes over the crossbar.
26:28 Christopher Samba takes a shot. Blocked by Matthew Upson.
25:49 The assistant referee flags for offside against Carlton Cole. Paul Robinson takes the free kick.
23:50 Corner taken right-footed by Mark Noble from the right by-line, Morten Gamst Pedersen makes a clearance.
23:39 Luis Jimenez takes a shot. Pascal Chimbonda gets a block in.
Correction - 22:40 Luis Jimenez takes a shot. Blocked by Pascal Chimbonda.
22:40 Luis Jimenez takes a shot. Pascal Chimbonda gets a block in.
21:19 Mark Noble gives away a free kick for an unfair challenge on Morten Gamst Pedersen. Morten Gamst Pedersen shoots direct from the free kick.
20:21 Foul by Matthew Upson on Jason Roberts, free kick awarded. Morten Gamst Pedersen crosses the ball in from the free kick, clearance by Matthew Upson.
19:15 Effort on goal by Carlton Cole from inside the penalty box misses to the right of the target.
17:55 Christopher Samba gives away a free kick for an unfair challenge on Carlton Cole. Mark Noble takes the direct free kick.
16:43 David Dunn fouled by Jonathan Spector, the ref awards a free kick. Paul Robinson takes the direct free kick.
16:17 The ball is sent over by Julien Faubert, save made by Paul Robinson.
14:22 Carlton Cole takes a shot. Morten Gamst Pedersen gets a block in.
12:37 Julien Faubert fouled by David Dunn, the ref awards a free kick. Julien Faubert takes the free kick.
11:31 Vincenzo Grella gives away a free kick for an unfair challenge on Junior Stanislas. Direct free kick taken by James Collins.
9:15 Close range effort by Jason Roberts goes wide of the left-hand post.
8:27 Direct free kick taken by David Dunn.
8:27 Booking James Collins receives a caution.
8:14 James Collins challenges Morten Gamst Pedersen unfairly and gives away a free kick.
7:09 Junior Stanislas crosses the ball, Headed effort from inside the area by Carlton Cole misses to the left of the goal.
6:32 The ball is crossed by Morten Gamst Pedersen, James Collins manages to make a clearance.
5:55 Corner taken by Morten Gamst Pedersen played to the near post, Mark Noble manages to make a clearance.
5:46 The ball is swung over by David Dunn, clearance made by Scott Parker.
5:12 Luis Jimenez challenges Keith Andrews unfairly and gives away a free kick. Paul Robinson takes the direct free kick.
2:43 Unfair challenge on Scott Parker by Jason Roberts results in a free kick. Direct free kick taken by James Collins.
1:04 Carlton Cole takes a shot. Comfortable save by Paul Robinson.
0:00 The referee gets the match started.
Live text and data provided by The Press Association.
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