City came from behind to beat Burnley 2-1 with two Sergio Aguero goals in the day's early kick-off, and Liverpool later edged above them on goal difference after Divock Origi and James Milner finally broke fierce Sunderland resistance at Anfield. But it was not all good news for Liverpool, who had Philippe Coutinho taken off on a stretcher.
The Brazilian suffered an ankle injury after a challenge from Didier Ndong late in the first half and left the stadium on crutches.
Coutinho's replacement Origi eventually broke fierce Sunderland resistance with a shot that looked more like a cross from the left of the area. Milner scored their second after Sadio Mane was fouled in the box.
At Turf Moor, Pep Guardiola made five changes to the Manchester City side that played in the Champions League in midweek, but he knows better than to start without Aguero.
The Argentine scored either side of halftime to take his tally to 33 in his last 34 games after Dean Marney put the home side ahead with his first league goal in seven years.
City have lost just one of their past 15 top-flight games, winning nine and drawing five, and Guardiola paid tribute to Aguero's influence.
"He played really well and moved really well. He had a really good game," said Guardiola. "From the beginning he was ready, his body language was very good."
The game of the day was at the Liberty Stadium where Swansea City won an astonishing see-saw encounter 5-4 against Crystal Palace with two goals from substitute Fernando Llorente in stoppage time to record their first win since the opening day of the season and first under manager Bob Bradley.
The result could have serious repercussions for Palace manager Alan Pardew, whose side are out of the relegation zone only on goal difference.
But at least his side showed spirit, turning round a 3-1 deficit to take a 4-3 lead before Llorente struck amid wild scenes.
There was more late drama at Leicester City, where Islam Slimani put away a 94th-minute penalty, Leicester's second of the match, in a 2-2 draw after Alvaro Negredo thought he had done enough to secure a rare Boro away win with goals either side of half time.
The bottom of the table is looking increasingly congested with just six points separating the bottom 10 teams.
Although Hull City remain in the relegation zone, a much improved second-half display saw them claim a 1-1 draw against West Bromwich Albion, with Michael Dawson equalising in the 72nd minute.
