Manchester City kept Premier League leaders Liverpool in their sights on Saturday 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 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 City went into their evening match against high-flying Chelsea 12 points behind the pacesetters.

Frank Lampard's men had the better of the early stages in Manchester and N'Golo Kante gave them a deserved lead midway through the first half.

But the lead lasted only eight minutes before Kevin De Bruyne equalised after a wicked deflection off defender Kurt Zouma left goalkeeper Kepa Arrizabalaga helpless.

Pep Guardiola's City were soon in the lead after Riyad Mahrez cut inside from the right to fire a low left-footed shot through Fikayo Tomori's legs and into the far corner and they held on to seal a vital 2-1 win.

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 top-flight 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," said Klopp. "We have a job to do to get results. We did that again.

"I have no problem that we were not brilliant today. You just have to make sure you are ready to fight for the result and we were that from the first minute."

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.

Mourinho effect

In the early kick-off at the London Stadium, Son Heung-min, Lucas Moura and Harry Kane were on the scoresheet for Spurs as Mourinho won his first game in charge 3-2 days after replacing the sacked Mauricio Pochettino.

The win -- the club's first away league victory since January -- will help to endear Mourinho to a sceptical Spurs support, who were sad to see Pochettino dismissed just six months after leading the club to a first-ever Champions League final.

“It was very, very important. Eleven months without music in the away dressing room, without a smile, without happiness and they did it," said the former Chelsea and Manchester United boss on ending Spurs' away-day blues.

“That's where I belong (on the touchline), that is my natural habitat," added Mourinho. "I just love it. When things go in your direction, winning is the best feeling."

Arsenal manager Unai Emery is under increasing pressure after another limp display. They are now winless in five Premier League matches.

Southampton took an early lead at the Emirates through Danny Ings only for Alexandre Lacazette to level.

James Ward-Prowse restored Southampton's lead in the second half but Lacazette saved Unai Emery's blushes with a goal deep into stoppage time.

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 bottom spot in the Premier League with a 2-0 victory away to Everton while Burnley won 3-0 at Watford, who are now bottom.

Ole Gunnar Solskjaer's Manchester United face Sheffield United on Sunday. (AFP)

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