Former Fulham striker Louis Saha scored against his old club but could not stop Manchester United falling further behind Arsenal in the title race. Saha ran onto to Cristiano Ronaldo's through-ball and unleashed a venomous 18-yard shot into the roof of the net.
But Fulham equalised when Luis Boa Morte drilled home a low shot.
United felt they should have had a penalty for a foul on Saha and Ruud van Nistelrooy, warming up as a substitute, was booked for running on to protest.
The draw now means United are a massive nine points adrift of Premiership leaders Arsenal, who beat Charlton at Highbury.
Sir Alex Ferguson freshened up his side after the midweek Champions League defeat to Porto by dropping Van Nistelrooy, Ryan Giggs and Tim Howard to the bench.
In came Diego Forlan, Darren Fletcher and Carroll and the visitors almost got off to the perfect start.
 | KEY MOMENTS 14 mins: Saha fires Man Utd into the lead 64 mins: Boa Morte levels for Fulham |
Forlan picked out Saha, but the Frenchman fired inches wide with only 10 seconds gone.
Ronaldo, starting in place of Ryan Giggs, roved around and showed some mesmeric skills, setting off on one jinking run that left Fulham's defence in disarray.
United were full of menace and constantly harried their hosts, in stark contrast to Wednesday's disjointed display.
It was only a matter of time before United made their superiority count, and they did so in breathtaking style.
United rampaged forward on the break, Carroll bowling the ball out to Ronaldo, whose beautiful through-pass found Saha.
The former Fulham man, showing impressive strength, took two touches and unleashed a powerful shot that left Edwin van der Sar with no chance.
For their part, Fulham gradually established a foothold on proceedings, and Sylvain Legwinski clipped the top of the United crossbar from Sean Davis' crossbar.
After the break, United maintained their high-tempo game and Ronaldo continued to bamboozle the Fulham rearguard with his fleet of foot.
He gave Moritz Volz a torrid time and was unlucky not to get a second for United as his shot bounced just the wrong side of the post.
But Fulham refused to buckle under the pressure and Adam Green sent a free-kick narrowly over United's crossbar.
Forlan should have done better than to head straight at Van der Sar from Ronaldo's cross.
And United were made to pay for their profligacy when Boa Morte banged in the equaliser after combining well with McBride.
The Portuguese international turned Wes Brown with a quick change of pace and struck a fierce shot that Carroll should have dealt with better.
The visitors were then denied a penalty when Saha was clearly brought down by Van der Sar after being put through by Forlan.
Van Nistelrooy and Giggs finally entered the fray on 70 minutes, but the duo had a limited impact as the game ended in a draw to leave United virtually out of touch of leaders Arsenal.
Fulham: Van der Sar, Volz, Goma, Pearce, Green, Malbranque (Inamoto 80), Sean Davis, Legwinski, McBride, Petta (Pembridge 66), Boa Morte.
Subs Not Used: Crossley, Knight, Rehman.
Booked: Sean Davis.
Man Utd: Carroll, O'Shea, Keane, Brown, Fortune, Fletcher (Giggs 72), Scholes, Phil Neville, Ronaldo, Saha, Forlan (van Nistelrooy 72).
Subs Not Used: Howard, Bellion, Djemba-Djemba. Booked: Brown, Forlan, van Nistelrooy.
Attendance: 18,306
Referee: A Wiley (Staffordshire).
MMIX
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It hurts a lot, but we really don't deserve to win anything this season
