Gabriel Jesus and Kevin De Bruyne scored either side of the interval, as Pep Guardiola’s men produced another scintillating performance.
Their city rivals, Manchester United, kept pace with a 4-1 win at home against Newcastle.
Dwight Gayle put the Magpies ahead, becoming the first player to score against Jose Mourinho’s men at home. However, goals from Anthony Martial, Chris Smalling and Romelu Lukaku gave the Red Devils all three points.
Chelsea climbed up to third place with a 4-0 thrashing of West Brom, leapfrogging Tottenham Hotspur who lost 2-0 at Arsenal in the early kick-off.
Liverpool are fifth after beating Southampton 3-0.Manchester
Crystal Palace were held to a 2-2 draw at Everton, Swansea City lost 2-0 at Burnley and Bournemouth hammered Huddersfield 4-0.