Brendan Rodgers’s Liverpool started the day in first place and they made an impressive start at the Etihad Stadium, with Philippe Coutinho giving the visitors a 24th-minute lead after a neat team move.
However, City captain Vincent Kompany headed home an equaliser seven minutes later and Alvaro Negredo put the hosts in front on the stroke of half-time with a tame shot that Liverpool goalkeeper Simon Mignolet could only palm into the net.
“The most important thing today was that we were losing 1-0 but we had the character and the trust to go for the win and we continued trying to attack,” said City manager Manuel Pellegrini.
“I think it was very important to try to finish the year near the top of the table.”
City ended the day as it started: in second place in the league. Arsenal is now leading ahead of city, with Liverpool dropping to fourth place behind Chelsea.
City, though, remain the favorites to repeat its 2012 title triumph after its ninth straight home win to start the season.
Pellegrini has now beaten every team in the top eight apart from Chelsea, and has netted a league leading 53 goals in 18 games.
Liverpool manager Brendan Rogers put on a brave face after the final whistle blew.
“We’re all very proud of the team tonight,” he said. “”I thought how we played — the charisma in our football, and the passing in our game — was exceptional.
“We’re bitterly disappointed not to win the game, but my overriding feeling is one of pride, because it was an outstanding performance.”