Scholes was dismissed for handball on the line in the 18th minute giving Danny Murphy the chance to put Fulham in front from the penalty spot and Rooney was red-carded for throwing the ball towards the referee after Zoltan Gera had made it 2-0.
After last week's 4-1 drubbing at home to Liverpool, United have now suffered back-to-back defeats in the Premier League for the first time since 2005.
The setback was softened later on Saturday as second-placed Chelsea wasted a chance to narrow the gap to one point by losing 1-0 at Tottenham Hotspur in a match delayed by a security scare.
Luka Modric's goal ended Chelsea boss Guus Hiddink's 100 percent record in the league since taking over in February.
The results made it a great day for Liverpool who host Aston Villa on Sunday knowing victory will see them breathing down the necks of a United side who seemed out of sight two weeks ago.
United lead the table with 65 points from 29 games while Chelsea have 61, having played a match more. Liverpool also have 61 points from 29 games played.
RELEGATION WORRIES
Arsenal consolidated fourth place with a 3-1 victory at Newcastle United that left the home side in the drop zone. The north London side have 55 points from 30 games.
Portsmouth eased their relegation worries with a 2-1 home win over Everton thanks to two Peter Crouch headers and Stoke City moved out of the bottom three with the 1-0 defeat of visiting fellow strugglers Middlesbrough.
Bottom club West Bromwich Albion look to be sliding towards the trapdoor after a 1-1 home draw with Bolton Wanderers.
Blackburn Rovers also drew 1-1 with visitors West Ham United.
United had not lost at Fulham since 1964 and recently won 4-0 at Craven Cottage in the FA Cup having registered a 3-0 win over the west London side at Old Trafford in the league.
However, the match swung Fulham's way when Bobby Zamora headed goalwards after Edwin Van der Sar had saved an effort by Brede Hangeland and instinctively Scholes used his hands to stop the ball going over the line.
Scholes was sent off before Murphy, a former Liverpool midfielder, placed his penalty beyond Van der Sar.
"That was a double blow, you miss a great player like Scholes and of course they got the penalty," United's Ryan Giggs told Sky Sports. "It knocked us off track a little bit.
"The lads were determined to get back on track but in the first half Edwin Van der Sar kept us in it. We were the better team by far in the second half."
United manager Alex Ferguson replaced the sluggish Dimitar Berbatov at halftime with Wayne Rooney to revive the visitors.
The champions duly pinned
