Philippe Coutinho scored a stunning winner 15 minutes from time as Liverpool made it 11 straight league matches unbeaten. Jordan Henderson had put the Reds in front in the the first half only for Edin Dzeko to level before the break.
“It’s a massive win for us,” Liverpool’s Adam Lallana told Sky Sports. “We’ve got momentum and they’re champions but I thought we thoroughly deserved it today.
“They came back into the game but the lads have got fighting spirit and the little magician (Coutinho) at the end came up with another wonderful goal. With players like that we’re going to go far.”
The win lifts the Reds level on points with fourth-place Arsenal, who host Everton later, while City remain five points behind Chelsea. The leaders also have a game in hand thanks to their appearance in Sunday’s League Cup final.
“It is three points less with one game less,” City manager Manuel Pellegrini said. “Of course it is difficult to reach the top of table if you lose three points.
“But we must keep going and try to return to our normal performance and see where it takes us.”
Liverpool started quickly with Lallana correctly ruled offside when he put the ball into the net after just 10 minutes.
The hosts took the lead moments later as City captain Vincent Kompany lost possession just inside his half. Raheem Sterling laid a ball wide for Henderson, who cut to the middle and curled a shot from outside the area into the top right corner.
“It was just a break and Raheem found me,” Henderson said. “I took a touch and thought ‘Have a go.’ Thankfully it went in.”
City almost drew level when Sergio Aguero hit the post after being sent through. The Argentine then set up Dzeko’s equaliser in 26th minute.
Aguero headed just over the bar in the opening moments of the second half and Lallana had another goal disallowed for offside against Martin Skrtel.
Liverpool then started to dominate and were rewarded with Coutinho’s long-range strike that gave keeper Joe Hart no chance.
Aguero and David Silva had late chances for City but shot wide. It summed up the visitors’ futility on the day as Dzeko’s goal was their only shot to hit the target.
Liverpool manager Brendan Rodgers lauded his team’s effort following a quick turnaround from their disappointing exit from the Europa League on Thursday.
“I’ve got to tip my hat off to the players,” he said. “To come out and play like that, how they’ve done today, just relentless they were.
“To restrict them to one shot on target, against a top team, I thought the players were incredible today. So they deserve all the praise they get for their performance and the result.”