Jose Mourinho's side fell behind thanks to another goal from the excellent Willian, but Romelu Lukaku - often maligned for not performing in the big games against the big teams - came up trumps to score and assist Jesse Lingard to hit the winner.
Chelsea were almost ahead within three minutes of the clash when Marcos Alonso volleyed a sizzling cross across the box, only for Alvaro Morata to crash his attempt off the bar from close range. That was the be the last thing of note to happen in the next 20 minutes as both sides worked their way into the game.
It was the Blues who looked the most lively, with Eden Hazard and Willian the stars who looked most likely to create an opening for Antonio Conte's side.
That opening came in the 31st minute when the pair combined excellently on the break. Willian carried the ball away from the Chelsea box and played in Hazard down the right side. The Belgian held on to the ball under pressure from Victor Lindelof and threaded a perfect through ball back to Willian, who United appeared to forget all about. The in-form Brazilian then fired straight through David de Gea at this near post - the Spaniard visibly frustrated with his efforts.
It was probably deserved, but United were level seven minutes later when Lukaku slotted home his 13th league goal of the season. The Belgian was found by Anthony Martial after Andreas Christensen clashed heads with the striker. And it was the Dane's grogginess that arguably allowed United access into the box, and Lukaku's finish was crisp.
Chelsea almost went 2-1 up when Alonso ghosted into the box after good play from the lively Hazard, but the Spaniard shot high and wide.
Both teams came out for the second half with the intention of trying to play, and players such as Paul Pogba, Martial and Morata came more and more into the game as time went on.
Danny Drinkwater had an effort on goal from distance which gave De Gea a little more trouble than perhaps it should have because of the sun. What would normally have been a routine save was almost spilled into the path of a lurking Alonso but Antonio Valencia was on hand to clear.
United almost took the lead through an incredible piece of acrobatic play from Lukaku. Alexis Sanchez's cross wasn't pinpoint, prompting the striker to adjust with a bicycle kick, which was just touched over by Thibaut Courtois.
The Red Devils did take the lead in the 74th minute through substitute Lingard - the England man was surprisingly able to peel off his marker, and he was found perfectly by Lukaku's curling cross from the right-hand side.
Chelsea had the ball in the back of the net through Morata in the 85th minute but it was controversially ruled out for offside. On another day though, the goal might have stood, with the Spaniard looking level.
It was a massive result for United, who now leapfrog Liverpool back into second place in the Premier League table, with Chelsea dropping down to fifth after Tottenham's victory over Crystal Palace earlier in the day.
It was a sweet victory for Mourinho after his recent war of words with nemesis Conte. His side will take huge confidence from the fact that they came from behind, and will seek to follow up the victory with another win over Crystal Palace next Monday.
Chelsea team: Courtois; Azpilicueta (c), Christensen, Rudiger; Moses, Drinkwater, Kante, Alonso; Willian, Morata, Hazard.— Chelsea FC (@ChelseaFC) 25 February 2018
Subs: Caballero, Cahill, Zappacosta, Emerson, Fabregas, Pedro, Giroud. #MUNCHE pic.twitter.com/OVUncUfBN2