Overshadowed by Robin van Persie this season, Rooney showed his predatory instincts after 79 minutes at Craven Cottage when he punished a defensive error to grab an unconvincing win that turned up the heat on Manchester City.
Faltering European champions Chelsea suffered their second late collapse this week, going down 3-2 at Newcastle United having led 2-1 with goals from Frank Lampard and Juan Mata.
Newcastle's new signing Moussa Sissoko equalised and then capped a superb home debut with a last-minute winner to increase the pressure on Chelsea's interim manager Rafa Benitez whose side conceded twice late on in a midweek draw at Reading.
Third-placed Chelsea have won only once in six games in all competitions and alarm bells are ringing about their hopes of sealing a top-four finish that brings a Champions League spot.
With Tottenham Hotspur playing on Sunday, Everton had a chance to move above them into fourth but had to fight back for a 3-3 draw at home to struggling Aston Villa, who led 3-1 before Marouane Fellaini's double spared the home side's blushes.
Lukas Podolski scored in the 78th minute to hand Arsenal a 1-0 win against visiting Stoke City, a result that helped the Gunners close in on the Champions League qualification places.
Despite a yawning gap at the top, Rooney said the title was far from being in the bag.
"We're in a good position but we're not getting carried away," he told ESPN. "Let's see where we are with three or four games to go."
United were not at their best and had an escape in the first half when Fulham's Brian Ruiz hit the inside of the post with a volley, although they carved out plenty of chances and Patrice Evra and Rooney were both denied by the woodwork.
A scrappy second half came to life late on when Fulham defender Philippe Senderos misjudged a high ball and Rooney raced clear to put United in front.
Van Persie was needed at the other end to clear a Senderos header off the line as United hung on for their 20th league victory of the season.
"I think it was a really determined performance and it wasn't easy because Fulham played their part. 1-0 doesn't do the game justice," said United manager Sir Alex Ferguson.
Any thoughts of putting some pressure on the Manchester clubs in the title race are long gone for Chelsea who were left reeling after another late horror show.
Benitez said his side should have been awarded a penalty and the hosts reduced to 10 men after striker Demba Ba, signed from Newcastle last month, was left bloodied by a clash with Fabricio Coloccini after trying to turn in a rebound before half-time.
"It was a penalty and a red card," Benitez told Sky Sports, saying Ba, who was replaced by Fernando Torres, had suffered a broken nose in the incident.
"If it had been in the middle of the park it would have been a free-kick and maybe a yellow but in the area it's a penalty and red because it was a clear chanc
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