City’s win gives them a two-point cushion over Chelsea and Tottenham 1-0 winners at West Ham, but Liverpool will join them on 23 points if they beat Huddersfield in the late kick-off.
Pep Guardiola’s side, who missed a late penalty to beat Liverpool at Anfield earlier this month, made it seven wins from nine league games as Burnley Goalkeeper Joe Hart endured a miserable return to his former club at the Etihad.
Sergio Aguero opened the scoring in the 17th minute before second-half goals rained in from Bernardo Silva, Fernandinho, Riyad Mahrez and Leroy Sane.
With the defending champions slipping ominously into gear, midfielder Kevin De Bruyne came on for just his second appearance of the season following a knee injury he suffered in August.
“After we scored the second goal and third it was much easier,” said Guardiola. “And of course, it’s good news that Kevin De Bruyne is back … The goals were so outstanding, beautiful, beautiful goals and three more points.”
Earlier, Ross Barkley scored in the sixth minute of injury time at Stamford Bridge to level the match at 2-2 after Anthony Martial had scored twice in the second half to cancel out Antonio Rudiger’s opener.
It was a bitter blow for the under-pressure United boss Jose Mourinho, returning to his former club after a poor start to the season and he lost his cool in emotional scenes in the final seconds.
Mourinho took exception to the celebrations of one of Chelsea’s backroom staff, Marco Ianni, who ran in front of the Portuguese on the touchline, as he seemed set for a desperately needed win.
But after the final whistle the United boss played down the incident, saying Ianni had apologised to him.
“(It was) not celebrations, but bad education. But I also made mistakes in football matches and I will make more so after the game when he came to offer his apologies, I accept,” added Mourinho.
The United boss, who has a tough run of fixtures coming up, including games against Juventus and Manchester City, described the 2-2 draw as an “awful” result for his team, who roared back from 2-0 down to beat Newcastle United in their last match.
Sarri said his side lost out to United in the physical battle as the game wore on.
“I am happy with the performance of the team for 60 minutes because for 60 minutes we played our football,” said the Italian.
“Then after the goal of 1-1 we haven’t played our football. We only played the long ball and we are not organised to go on the second ball.”
Erik Lamela struck with a cool header late in the first half at the London Stadium to give Tottenham their fourth successive league victory.
That made it five goals in just eight appearances this season for Lamela, who was making only his second league start of the campaign.
Liverpool travel to Huddersfield looking to end a four-game winless run in all competitions following an electric start to the season.
Elsewhere, Cardiff beat Fulham 4-2 to lift themselves off the foot of the table.
Newcastle are now languishing in bottom spot after a 1-0 home defeat against Brighton while Watford beat Wolves 2-0 and Bournemouth played out a goalless draw with Southampton.