Former Chelsea striker Romelu Lukaku scored and then created the winning goal against his old team at Old Trafford on Sunday.
The win put United back in second place in the Premier League, still 13 points behind neighbours Manchester City, while Chelsea drop below Tottenham into fifth place.
Chelsea were the brighter team early on and Alvaro Morata, brought back into the side, volleyed against the bar after only four minutes.
The Londoners deserved the lead that Willian gave them after 31 minutes, taking Eden Hazard's pass and beating David de Gea at his near post.
As United improved, Lukaku belied his reputation for not scoring against the big clubs by equalising before halftime, then crossed perfectly for substitute Jesse Lingard to head the winner in the 75th minute.