Pep Guardiola's rampant aspect scored four times in the starting 25 mins of a Christmas cracker at the Etihad Stadium.
Kevin De Bruyne struck first earlier than Riyad Mahrez converted a penalty.
Ilkay Gundogan bagged City's third and Raheem Sterling scored a penalty of his personal.
James Maddison, Ademola Lookman and Kelechi Iheanacho all netted for Leicester within the space of simply 10 mins early in the 2d 1/2.
But Aymeric Laporte killed off the traffic' hopes of an exceptional get away act by means of heading City's 5th purpose earlier than Sterling scored again inside the final minutes.
It became the highest scoring suit in the top-flight on Boxing Day considering Manchester United won 6-three towards Oldham in 1991.
With 2nd located Liverpool's fit in opposition to Leeds on Sunday postponed because of the coronavirus, City have been capable of expand their lead over their principal identify competitors.
Guardiola's champions have won nine successive league games, scoring 17 desires of their final 3 matches as they quit 2021 in scintillating fashion.
City's four-0 win towards Newcastle last weekend made them the first pinnacle-flight team to win 34 league video games in a calendar yr, beating Liverpool's 1982 record.
A 36th league victory at Brentford on Wednesday might ship City into the brand new 12 months firmly cemented as identify favourites.
