City manager Pep Guardiola's proclamation that if his side drops points it would leave the title race "finished" suggests the champions will go all out for a win at Etihad Stadium.
The former England striker slotted a low finish past goalkeeper Jordan Pickford and celebrated his 58th-minute goal with a somersault.
Pierre-Emerick Aubameyang wrapped up a routine victory in the 84th minute with his 14th goal of the campaign, leaving him the league's top scorer.
Second-placed Tottenham dropped nine points behind Liverpool, who won 5-1 at home to Arsenal.
Liverpool are blowing away teams, with this ninth straight win coming three days after a 4-0 victory over Newcastle United.
Klopp's side is four points in front of second-placed Manchester City after 18 of 38 Premier League matches as it looks to become champion of England for the 19th time.
The Armenia playmaker fractured a metatarsal in Wednesday's 2-0 League Cup quarter-final defeat by neighbour Tottenham.
While Vardy's lone goal saw Leicester hand Chelsea their first home defeat this season, Hodgson's Palace stunned Pep's City 3-2 to end their 100 per cent home record.
Solskjaer was hired as manager until the end of the season on Wednesday in a sentimental choice likely to prove popular with United's increasingly disillusioned fan base.
Police are reviewing footage that circulated widely online during Chelsea's 2-0 win over City on Saturday, showing a man aggressively hurling abuse at Sterling as the player retrieved the ball off the field.
Romelu Lukaku ended his 997-minute wait for a goal at Old Trafford in the 42nd.
Lucas Torreira acrobatically volleyed into the bottom left corner in the 83rd minute to score the lone goal.
Despite a hint of offside, Salah broke the deadlock midway in the 25th minute as he tucked away a parried shot.
Addressing what he describes as "rumours" of Mourinho leaving United, Jorge Mendes says "it's totally untrue. Jose is very happy at the club and the club is very happy with him."
It was the first United-Arsenal game since 1986 that didn't have either United manager Alex Ferguson or ex-Arsenal coach Arsene Wenger in the dugout. Ferguson was in the stands, however.
The changes in personnel had little effect on Guardiola's well-oiled machine, and only the brilliance of Watford goalkeeper Ben Foster ensured City didn't head into the interval with more than a one-goal advantage.
Klopp said immediately after the Merseyside derby that he regretted his actions and had apologized to Everton manager Marco Silva.
Arsenal's board may have a big decision to make in a few weeks, with the midseason transfer window opening on January 1.
The team has won one of its 14 league games this season, and that came victory came on September 1.
With Tottenham losing 4-2 at Arsenal later Sunday, Chelsea moved back up to third place.
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