United, who host Chelsea in the second leg of their Champions League quarter-final on Tuesday, rested several first-choice players and had just the sort of undemanding afternoon they wanted as first-half goals by Dimitar Berbatov and Antonio Valencia proved decisive at Old Trafford.
Chelsea moved up to third on 58 points after a 67th-minute Florent Malouda goal was enough to beat bottom club Wigan Athletic 1-0 at Stamford Bridge.
Manchester City, who visit Liverpool on Monday, have 56 points, three clear of Tottenham Hotspur who beat Stoke City 3-2.
With Wayne Rooney suspended, United manager Sir Alex Ferguson still felt able to make seven other changes from the team who won 1-0 at Chelsea in the Champions League last week.
Fulham had won one away game all season while United went into the match with 14 wins and a draw from 15 at home and those numbers proved a reliable form guide.
United went ahead after 12 minutes when Nani slid a cross into the path of Berbatov, who slotted his 22nd of the season.
Nani was the provider again after 32 minutes when his shot was deflected towards Valencia who had a simple header.
"It was an important win and at this stage of the season that's the name of the game," Ferguson told Sky Sports.
"We didn't play well, we were a bit wasteful with our possession in the second half. We had great opportunities to add to the goals but we didn't take them and we had to hang on a little bit at the end."
A year ago it was Chelsea charging and they went on to wrap up the title in style with an 8-0 thrashing of Wigan.
They beat them 6-0 away earlier in the season too but there was not such an obvious gulf in class on Saturday. The champions were always on top but huffed and puffed for long periods.
With Fernando Torres starting on the bench it was Didier Drogba and Malouda who carried the most danger but goalkeeper Ali Al Habsi was equal to their best efforts.
However, he was at fault for the goal when he flapped at a David Luiz header from a corner and Malouda tapped in.
"They put a lot of pressure on us and we were not able to play our football and the first half was not so good," said Chelsea boss Carlo Ancelotti.
"The game was between the (Champions League) quarter-final so it was difficult to stay in focus but the second half was better. Wigan lost a bit of energy and we won a difficult and a very important game."
Peter Crouch, whose early red card on Tuesday played a big part on Tottenham's 4-0 Champions League defeat at Real Madrid, did his best to get the fans back onside
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