Rooney's 21st top-flight goal of the season, which arrived towards the end of the first half, proved enough to see off spirited mid-table opposition.
The result sent Sir Alex Ferguson's side, who have won their last six league games, three points clear of neighbours Manchester City at the top of the table with eight games remaining.
It was far from vintage United, but with their next four games against teams in the bottom six, it is difficult to see where United are going to slip up.
"For an hour we played very well and we made some decent opportunities but you have to give credit to Fulham," Ferguson told Sky Sports.
"They had more left than we did in the last 15 minutes. I think they had a claim (for a penalty), there's no doubt. We had a claim in the first half. Maybe the referee was thinking about that, but certainly Michael Carrick caught Danny Murphy's heel."
Having destroyed struggling Wolves 5-0 in their last outing, United were hoping Fulham would prove equally obliging opponents with the league delicately poised.
Fulham spent the opening exchanges penned inside their own half.
But this was a night for patience as United struggled to impose themselves until Rooney struck three minutes before the interval.
Veteran midfielder Ryan Giggs headed an early chance straight at keeper Mark Schwarzer while Patrice Evra proved an unlikely goal threat in the 32nd minute with an overhead kick which flashed narrowly wide.
But the ruthless finishing which was so evident eight days earlier at Molineux was missing as Fulham created just as many chances as United before the interval.
Not for the first time this season, Clint Dempsey was his team's main goal threat.
The United States international twice tested David De Gea in the space of a few minutes, his second effort a lovely attempted curler from the edge of the area which had United's Spanish keeper diving at full stretch to claw away.
Yet just when Fulham thought they had survived the opening half without damage, Rooney pounced from close range after Jonny Evans had teed-up the striker from Ashley Young's 42nd minute cross following a mistake by John Arne-Riise.
The sighs of relief could be heard all around the ground.
United, who meet City in what could be a winner-take-all game on April 30, dominated possession after the interval but were unable to add to their tally.
Schwarzer was forced into action when Giggs played the ball over the top for Antonio Valencia, who seemed likely to score, but his shot was straight at the Australian international.
With 15 minutes remaining, United spurned a glorious chance to double their advantage.
Schwarzer, who had an excellent game, twice denied Young before Giggs had a goal-bound effort blocked by Brede Hangeland.
United survived a scare in the 89th minute when Fulham substitute Danny Murphy went crashing inside the penalty area following a Michael Carrick challenge.
But referee Michael Oliver waved away Fulham's appeals for a penalty as United hung on for their ninth win in 10 league games.
Fulham manager Martin Jol thought that it had been the wrong decision.
"I feel it was a difficult decision, it always is for a penalty," said the Dutchman.
"I think you should send Michael Carrick off and I think everyone in the stadium was expecting it. I've seen it many times before, you have to be brave to give a penalty like that here."
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