The hosts controlled the possession in the early stages but were behind after 11 minutes when Wayne Rooney headed into his own net from a dangerous Charlie Adam corner.
© PA Photos
Stoke were encouraged by the opening goal but failed to add to their advantage, allowing United to come back into the game.
Rooney was able to atone for his earlier error in the 27th minute by heading in from close range following a beautifully directed cross from Robin van Persie.
The hosts continued to dominate following the equaliser and managed to sneak ahead before half-time when Antonio Valencia's low cross found Van Persie at the back post and he was able to finish the move smartly.
It was Rooney's turn to become provider at the beginning of the second period as he picked out Danny Welbeck with a dangerous delivery to give the England forward the simple task of heading past Asmir Begovic.
Jonny Evans should have extended the lead just moments later but his header was somehow pushed to safety by Begovic.
The visitors managed to pull a goal back on the hour mark through Michael Kightly, as the former Wolverhampton Wanderers forward travelled into the United half unchallenged before striking the ball past De Gea.
Rooney ended all hopes of a Stoke fightback when he finished well at the back post after the visitors failed to clear a Van Persie corner.