After 10-man Chelsea was contentiously held to 1-1 by Burnley, City trimmed the gap on the leader to five points by sweeping aside Newcastle 5-0.
Sergio Aguero put City in front inside two minutes with a penalty, then Samir Nasri and Edin Dzeko scored in the next 20 minutes. David Silva completed the rout with quick-fire goals at the start of the second half as City cut Chelsea's goal advantage to three in the title race with 12 games to go.
Chelsea had led through Branislav Ivanovic's first-half opener, but Ben Mee headed in Burnley's lever after key midfielder Nemanja Matic was sent off.
United lost for only the second time since November — and could find itself out of the Champions League qualification places by the end of the weekend — as Swansea came from behind to win 2-1.
Arsenal jumped ahead of United into third place with a 2-1 win at Crystal Palace thanks to goals by Santi Cazorla, from the penalty spot, and Olivier Giroud. Fifth-place Southampton hosts Liverpool on Sunday.
Tim Sherwood made a disappointing start to his managerial career at Aston Villa, with the team losing 2-1 at home to Stoke to stay in the relegation zone and drop below Burnley on goal difference.
Queens Park Rangers is only out of the bottom three because of goal difference after losing 2-1 at Hull. The London club's midfielder, Joey Barton, was sent off in the 32nd minute for hitting out at two opponents, and Hull scored an 89th-minute winner through Dame N'Doye.
Sunderland went three points ahead of QPR by drawing 0-0 with West Bromwich Albion.
The game at Stamford Bridge added to manager Jose Mourinho's sense of injustice over refereeing decisions.
Matic, who has been one of Chelsea's most important players, will miss next weekend's League Cup final against Tottenham as well as league games against West Ham and Southampton following his red card.
Ashley Barnes escaped punishment in the 70th for a high challenge on Matic, who then angrily pushed the Burnley striker and received a straight red card. Chelsea also had two strong penalty claims dismissed.
It is only the second time Chelsea has dropped points at home in the league.
City's victory was the ideal warm-up for the first leg against Barcelona in the last 16 of the Champions League on Tuesday. And it's now nine goals in two games for City following a 4-1 victory over Stoke.
Dzeko, whose place in City's attack seems under threat following the signing of Wilfried Bony, earned the penalty after being tripped by Vurnon Anita after 24 seconds. Aguero's successful spot kick was the striker's 22nd goal of the season.
Dzeko's deflected pass then fell into the path of Nasri, who shot into the roof of the net in the 12th. Dzeko grabbed the goal his contribution merited in the 21st when he sidefooted past goalkeeper Tim Krul.
At the start of the second half, Nasri squared to Silva, who netted from close range, and fired in a low shot within two minutes.
It was a miserable day for City's neighbours. United went ahead in the first half through Ander Herrera but midfielder Ki Sung-yueng equalized two minutes later, and Jonjo Shelvey grabbed the winner with a 25-meter shot.
Since losing at Manchester City on Nov. 2, United's only defeat in 20 matches had come at home to Southampton.
AP Sports Writer Steve Douglas in Manchester contributed to this report.