United opened the scoring through Scott McTominay's early strike, with Cristiano Ronaldo claiming the assist, following good work by Mason Greenwood.
The lead was doubled when Jadon Sancho took up Luke Shaw's invitation to drive into the box and thought he had his maiden goal at Old Trafford, only for the Premier League to rule it as an own-goal by Ben Mee.
Ronaldo got in on the act by stabbing in the rebound after Wayne Hennessey tipped a McTominay drive onto the woodwork, although Aaron Lennon soon reduced the arrears.
The second half was a more sedate affair, although McTominay again brought the best out of Hennessey, making his Premier League debut for the Clarets, with another raking drive.