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.
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.
"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.
"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.
"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
