The defending champions withstood an early second-half onslaught from Leicester City before then blowing the Foxes away with a 6-3 win. Elsewhere, Chelsea rallied from a goal down to beat Aston Villa 3-1.
Kevin De Bruyne set the tone for City in the fifth minute of their Boxing Day encounter against Leicester, when he brought Fernandinho hoofed pass down perfectly before spinning away from Jannik Vestergaard and finding the bottom corner.
De Bruyne’s early effort was compounded by Riyad Mahrez’s spot-kick in the 14th minute – the first of two Youri Tielemans would give away on the night. By the time Ilkay Gundogan scored the third in the 21st minute, a tap in after Kasper Schmeichel had palmed the ball into his path, City were cruising.
A fourth from Raheem Sterling – from the spot – meant that City took a four-goal lead with them into the break. However, the Foxes rallied back after the interval and cut the deficit to one with three goals between the 55th and the 65th minutes. Former City man Kelechi Iheanacho played a starring role in the mini-comeback, creating a goal each for James Maddison and Ademola Lookman before firing one himself.
However, Aymeric Laporte headed City clear in the 69th minute from a corner, and Sterling completed his brace three minutes from time as Pep Guardiola’s men picked up yet more points.
Elsewhere, City’s title rivals Chelsea were at risk of falling apart before the clock marked half-an-hour of football played at Villa Park. A whipped Matt Targett delivery was headed past Edouard Mendy by his teammate Reece James, which meant that Aston Villa had the lead against the run of play.
However, Chelsea were level just five minutes later through Jorginho, who scored from the spot after Matty Cash had brought Callum Hudson-Odoi down inside the box.
Thomas Tuchel sent on record-signing Romelu Lukaku for the second half, and the move paid dividends. The Belgian headed Chelsea in front in the 56th minute from a Hudson-Odoi cross before winning a spot-kick in the 92nd minute for Jorginho to convert – ensuring that the Blues returned home with maximum points.