City's 100 per cent Premier League record at the Etihad Stadium this season was under threat when Philippe Coutinho put Brendan Rodgers' in-form side in front.
However, free-scoring City were a constant threat in the first half and moved ahead by the break courtesy of goals from skipper Vincent Kompany and Alvaro Negredo.
Liverpool posed plenty of questions thereafter, demonstrating why they topped the table prior to Thursday's game, but City held on for three precious points.
The victory leaves Pellegrini's charges second in the top flight, just a point behind leaders Arsenal, and the Chilean was pleased with the manner in which his players reacted to going behind.
He said: "It was very important because Liverpool were the best team in the Premier League. They were top of the table before the match so if they won they would be four points in front of us.
"It was very important, especially when we were losing 1-0, the personality of the team to go for the game.
"I'm very happy with our response, because it's not easy when you play such a difficult team who can play on the counter-attack when you are losing 1-0. It's very easy for them to have space, but we defended very well."
Just three points seperate the top four teams in the Premier League and Pellegrini is predicting an enthralling race for the title.
He said: "It's just half of (the) Premier League (season completed); we have the second half that will be very close with five or six teams going for the title."
