United started the match the stronger with Wayne Rooney dictating much of the early tempo. Ryan Giggs had the game's first effort on target, after 11 minutes, when he headed a Rafael cross into the arms of Mark Schwarzer.
The away side began to enjoy a period of possession as the 20-minute mark approached, however, with Moussa Dembele firing wide from the edge of the area, before Clint Dempsey tested the palms of David de Gea.
Antonio Valencia so nearly opened the scoring after 30 minutes when he drove into the area, but his effort was collected by Schwarzer.
Patrice Evra was next to go close for the home side with an overhead kick inside the box, but it drifted just wide.
United began to gain control of the match once more as the half progressed, and took the lead five minutes before the break when Rooney converted an Ashley Young cross at the far post.
Valencia so nearly extended United's lead moments into the second period, but Schwarzer pushed the winger's effort away from close range, before Aaron Hughes almost found his own net.
Young brought a fine save from Schwarzer after 52 minutes as the champions looked for that second strike.
Giggs fired wide with 20 minutes remaining, before Young and Giggs so nearly added a second five minutes later.
Fulham remained a threat, however, and came close via Dempsey with little over ten minutes remaining.
The away side had a strong penalty shout turned down late on when Danny Murphy tumbled in the area, but the referee waved play on, as United held on for a welcome three points.
Next up for United is Blackburn away next Monday, while Fulham host Norwich City on Saturday.