Liverpool blew at 2-0 lead at Anfield as Brighton battled back to earn a deserved 2-2 draw.
City are now five points off the top after Pep Guardiola’s 10 men were beaten 2-0 by Crystal Palace at the Etihad.
United were humiliated 5-0 at Old Trafford by Liverpool last weekend to leave manager Ole Gunnar Solskjaer hanging on to his job.
But the Norwegian’s decision to switch to a back three and start with a veteran strike pairing of Cristiano Ronaldo and Edinson Cavani paid off.
Ronaldo’s sumptuous volley from Bruno Fernandes’ cross settled United’s nerves six minutes before half-time.
The five-time Ballon d’Or winner then turned provider for Cavani to dink the ball over Hugo Lloris.
Marcus Rashford came off the bench to round off a badly-needed three points and performance for Solskjaer’s men, who registered just a second clean sheet in 22 games.
“We’ve built this performance on hard work, discipline and keeping the ball away from our goal,” said Solskjaer.
Chelsea extended their lead at the top to three points as Reece James scored twice in a 3-0 win at Newcastle.
The Magpies are hoping to follow in the footsteps of Chelsea and City’s success following huge investment from foreign owners.
However, Saudi-owned Newcastle have a battle just to remain in the top flight as they remain rooted in the bottom three without a league win this season.
All the goals arrived in the second-half as James produced two stunning finishes from right wing-back before Jorginho’s penalty rounded off the scoring.
“It will never be the moment when we celebrate results on the other pitches,” said Chelsea boss Thomas Tuchel. “It’s first of all far too early and second, we want to focus on ourselves.”
‘It feels like defeat’
Liverpool stretched their unbeaten run to 24 games in all competitions, but will feel two points slipped away after another flying start.
“It feels like a defeat,” said Liverpool manager Jurgen Klopp. “In the second-half, we were not good enough. The body language I didn’t like it all.”
Mohamed Salah’s scoring streak came to an end at 10 games, but the Egyptian set up the opener as his pass was swept into the far corner by Jordan Henderson.
Sadio Mane doubled the home side’s advantage with a back post header before the Senegalese had another goal ruled out for handball after he caught Brighton goalkeeper Robert Sanchez in possession.
The Seagulls grabbed a lifeline before half-time when Enock Mwepu’s cross flew over the stranded Alisson Becker.
Brighton snatched a point when Leandro Trossard rounded off a brilliant team move 25 minutes from time.
City’s first home defeat of the season rounded off a perfect day for the Chelsea in the title race.
Wilfried Zaha punished slack defending from Ruben Dias and Aymeric Laporte to fire into the far corner after six minutes.
Laporte was then sent off for pulling down Zaha as the last man in first-half stoppage time.
Gabriel Jesus thought he had equalised midway through the second half only for the goal to be ruled out for offside against Phil Foden.
The 10 men were then caught out two minutes from time when Conor Gallagher smashed high past Ederson.
“It went wrong in many, many things and we lose the game,” said Guardiola.
Arsenal are up to sixth after a fast start and some inspired goalkeeping from Aaron Ramsdale earned the Gunners a 2-0 win at Leicester.
Gabriel and Emile Smith Rowe struck inside the opening 18 minutes for the visitors at the King Power.
But they relied on Ramsdale thereafter as the England international made a miraculous save from James Maddison among a string of impressive stops.
Burnley registered their first win of the season in style with a 3-1 victory over Brentford to move out of the bottom three.
Southampton opened up a four-point cushion over the relegation zone thanks to Che Adams’ strike in a 1-0 win at Watford.