Old Trafford was not the easiest place for Brian Laws to go in his first game in charge but his side made the reigning champions work for the points and in the end the result flattered them.
The Clarets had the best chance of the first half when a superb counter-attack resulted in Steven Fletcher dragging a close-range effort wide of the target.
Sir Alex Ferguson's side were not without opportunities however, most of which came through Antonio Valencia who shone on the right flank. Dimitar Berbatov saw a half-volley clip the outside of the post while Luis Nani squandered several shots.
The sides went in level at the break but Berbatov gave United the lead 18 minutes into the second half as his strike deflected off a white shirt and spun past a helpless Brian Jensen.
Just moments later the Bulgarian's low effort was pushed by Jensen into the path of Wayne Rooney who tucked his 16th goal of the season into the bottom corner.
Senegalese forward Mame Diouf came on for the England hot-shot and made a name for himself in injury time as he steered home a Valencia cross with a glancing header.
The visitors came close to getting goals back through David Nugent and Steven Thompson who saw a headed effort hit the post. Wade Elliott also saw a strike blocked on the line by Gary Neville, though questions may be raised as to whether the skipper used his hand in the act.