Goals from Emre Can, Dejan Lovren, Joel Matip and Roberto Firmino secured the Reds' fifth win in six league games and only goal difference now separates City, second-placed Arsenal and Liverpool in third.
Despite their brilliance in attack, Liverpool's defence remains a weakness, with Lovren twice allowing James McArthur to level before the break.
It was a wonderfully entertaining match, with the opening 45 minutes particularly pleasing on the eye as defensive mishaps and attacking verve resulted in five goals - the most in a first half in the Premier League this season.
Indeed, the first three goals in a breathless encounter came within a hectic spell of five minutes and 45 seconds.
Source: BBC Sports