It is now 14 goals this season for the defending champions after a 4-0 home win over Brighton that included a double from Sergio Aguero, the league's top scorer with six.
City's win was marred by a first-half injury to arguably the team's best defender, Aymeric Laporte, which according to manager Pep Guardiola could keep the centre back out for "a while".
Meanwhile, pre-season predictions that this will be a transitional year for United and Chelsea under inexperienced managers are proving true, with the two teams already seven points off Liverpool before September with just one win apiece.
Both squandered leads, United failing to build on Daniel James' early goal — his third of the season following his off-season arrival from second-tier Swansea — and drawing 1-1 at Southampton.
Chelsea will be even more unhappy, surrendering a two-goal lead at home to promoted Sheffield United and drawing 2-2.
Every weekend has featured some sort of contentious issues with VAR, being used for the first time in the Premier League this season, and the latest dispute was at Crystal Palace's 1-0 win over Aston Villa.
Villa thought they had equalised in the seventh minute of stoppage time through Henri Lansbury, only for the goal to be ruled out because teammate Jack Grealish was adjudged to have dived in the build-up. Villa's players were furious and it looked a tight call, with the video assistant referee choosing not to overturn the referee's on-field decision.
A touch of fortune and a defensive error helped Liverpool ease to a 13th straight win.
Trent Alexander-Arnold's cross from the right glanced off the back of Burnley's New Zealand striker Chris Wood and spun high and beyond the reach of goalkeeper Nick Pope into the far corner of the net in the 33rd minute.
Four minutes later, Burnley defender Ben Mee passed the ball straight to Roberto Firmino in midfield and the Brazil forward played in Sadio Mane, who slotted home. Firmino added the third in the 80th minute from a counter-attack.
Manchester City's third victory in four matches might have come at a huge cost with the right knee injury to Laporte.
The French defender, called up by his national team on Saturday for just the second time, punched the ground as soon as he made contact with Adam Webster as the Brighton centre back charged down the right wing. Laporte held his hands behind his head and shook his head as he was carried off.
"It doesn't look good," Guardiola said. "I'm waiting for the doctor to call me. He [Laporte] might be out for a while."
Any lengthy absence for Laporte would be a major blow to City, who released long-serving captain Vincent Kompany in the off-season and have John Stones out injured. Fernandinho, a centre midfielder, filled in as a centre back off the bench against Brighton.
Kevin De Bruyne and substitute Bernardo Silva were the other scorers for City.
The sight of Paul Pogba hobbling away from St Mary's stadium was a further blow to United after their poor display against Southampton.
United manager Ole Gunnar Solskjaer said Pogba "got a bad knock on his ankle" but expected the midfielder to still turn up for international duty with France this week.
James' goal was cancelled out by Jannik Vestergaard's header in the 58th minute. Kevin Danso was handed a second yellow card for a crude, high challenge on Scott McTominay, reducing Southampton to 10 men in the 73rd minute, but United couldn't capitalise.
- AP
