London: Manchester City kept Premier League leaders Liverpool in their sights after battling back to beat Chelsea as Jose Mourinho ended Tottenham's away-day woes in his first game in charge.
Leicester saw off Brighton 2-0 on Saturday to stay in second place, eight points behind Jurgen Klopp's men, while struggling Arsenal needed a stoppage-time goal to draw 2-2 with lowly Southampton.
Liverpool's hard-fought 2-1 win at Crystal Palace meant defending champions City went into their evening match against high-flying Chelsea 12 points behind the pacesetters.
N'Golo Kante gave the visitors a deserved lead midway through the first half at the Etihad but City hit back with a deflected shot from Kevin De Bruyne and a trademark Riyad Mahrez strike to win 2-1.
Pep Guardiola's men were never entirely comfortable with a one-goal lead but their margin of victory could have been greater as Raheem Sterling found the bottom corner deep into stoppage time, only for VAR to rule the goal out for offside.
City's possession figure of 46.74 percent is the lowest recorded by a side managed by Pep Guardiola in any of his 381 top-flight matches in charge.
"It was a top game against a top side," Guardiola told Sky Sports.
"Chelsea have been big quality for the past 20 years. When they went ahead in the best moments they had we scored through Kevin De Bruyne. Then we missed a lot of chances." Guardiola sounded the alarm over all-time top-scorer Sergio Aguero, who limped off in the second half, saying he feared his injury could be "bad".
Liverpool late show
Earlier, Liverpool once again demonstrated their knack for scoring last-gasp winners, with Roberto Firmino finishing from close range following a goalmouth scramble.
Liverpool had looked set to drop points for just the second time this season after Wilfried Zaha cancelled out Sadio Mane's opener in the 82nd minute.
The European champions, chasing their first league title for 30 years, have now won 12 of their 13 Premier League matches this season and are unbeaten in 30 league games.
"We are not out there to show we invented football. We have a job to do to get results. We did that again," said Klopp. Brendan Rodgers' Leicester kept up their dogged pursuit of the leaders, with second-half goals from Ayoze Perez and Jamie Vardy giving them a fifth successive league win.
In-form Wolves won 2-1 at 10-man Bournemouth courtesy of a Joao Moutinho free-kick and Raul Jimenez's goal to climb to fifth in the table.
Norwich lifted themselves off the bottom with a 2-0 victory away to Everton while Burnley won 3-0 at Watford, who are now bottom.
What they said...
It was a top game against a top side – Pep Guardiola City manager
Chelsea have been big quality for the past 20 years. –Kevin De Bruyne City player
We are not out there to show we invented football. –Jurgen Klopp Liverpool manager
Elsewhere...
Arsenal: 2 drew with S’thampton: 2
Bournemouth: 1 lost to Wolves: 2
Brighton: 0 lost to Leicester: 2
Everton: 0 lost to Norwich: 2
Watford: 0 lost to Burnley: 3
West Ham: 2 lost to Tottenham: 3