Manchester United went three points clear at the top of the Barclays Premier League after at Old Trafford.
The win was United's sixth consecutive in the league as they now hold an edge on local rivals Manchester City in the fight for the title.
United started with Ashley Young restored to the side on the left flank with Welbeck moving up front and Javier Hernandez dropping to the bench.
Fulham started with 18-year-old Kerim Frei, in what was only the midfielder's third Premier League start.
After an fairly even first period, United took the lead three minutes before half time.
A trademark in-swinging cross by Ashley Young somehow failed to be cleared by John Arne Riise, allowing the ball tor reach Jonny Evans at tha back post. Stretching in front of goalkeeper Schwarzer, Evans was able to turn the ball back for Rooney, who calmly side-footed the ball high into the net.
The goal was Rooney's 21st goal in the Premier League this season and gave United a huge psychological edge, as well as the obvious advantage on the score sheet, heading into the break.
United came desperately close to putting the result beyond doubt 15 minutes from the end. Mark Schwarzer had to be at his best to deny Young from making it 2-0.
But with the score remaining at just 1-0 tension began to build both on and off the pitch at Old Trafford with all realizing the possible consequences of dropping two points at this stage of the season.
And with just two minutes to go that nervousness reached fever-pitch as Fulham had a huge appeal for a penalty turned down. Referee Michael Oliver deeming that Michael Carrick's challenge on Danny Murphy was not a foul.
Despite the uneasiness United held on to get the all-important three points.
The Red Devils now have a full week off before taking on relegation-threatened Blackburn at Ewood Park.
The big fixture on the horizon remains the trip to the Etihad to face second-place City at the end of April. United will be hoping that win there will seal their retention of the Premier League title.