Chelsea were much the better side in the first-half, but mistakes cost the away side as United's quick counter-attacks punished Frank Lampard's side on Sunday afternoon.
Marcus Rashford was the double, one from the spot and one midway in the second-half to send United well on their way to all three points.
Anthony Martial was also on the scoresheet after he was found free at the back post and tapped into an empty net.
But Dan James stole the headlines. Ole Gunnar Solskjaer gave the Welshman game time towards the end and the midfielder scored on his Premier League debut, and dedicated his goal to his late father who passed away a few weeks ago.