The north Londoners fall behind to Leicester's early goal at the King Power Stadium, but they managed to take three points with three goals of David Luiz, Alexandre Lacazette and Nicolas Pepe.
Rayan Ait-Nouri’s goal set Wolverhampton Wanderers on the way to a deserved victory over Crystal Palace, putting them level on points in the Premier League's top three.
Liverpool have 86 points from 31 games with Manchester City trailing by 23 points ahead of their trip to Chelsea.
Liverpool stretched their Premier League lead to 13 points by outclassing second-placed Leicester in a 4-0 win on Boxing Day as Manchester United and Tottenham cut the gap on fourth-placed Chelsea.
In other games, Arsenal dented Chelsea’s increasingly fragile title pursuit with a 2-0 derby win while Manchester United continued their stirring revival under Ole Gunnar Solskjaer with a 2-1 victory over Brighton & Hove Albion.
Huddersfield frustrated the bid by Pep Guardiola's runaway champions to set new Premier League records for the most goals, points and wins in a season.
Manchester United has regained second place in the Premier League with a routine 2-0 home win over Swansea City, hours after Liverpool deposed them with a 2-1 victory at Crystal Palace.
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