Luis Diaz spared Liverpool a rare Anfield defeat, but a 1-1 draw with Tottenham on Saturday represents a major blow to the Reds' title ambitions.
Son Heung-min left the famous old stadium shaken early in the second half when he tucked in from close range to give Antonio Conte's visitors a shock lead.
That was his 20th league goal of the season, and Liverpool knew anything other than a win would put City within sight of the Premier League trophy.
Liverpool have an unprecedented quadruple in their sights, and Diaz's deflected strike for an equaliser in the 74th minute just about kept the dream alive, but hopes might be fading. They go top for now, level on points with a City side who have a game in hand, against Newcastle United on Sunday.
Mohamed Salah and Harry Kane had early shots blocked, before Virgil van Dijk nodded wide after getting on the end of an outswinging Andy Robertson corner from the left.
A misdirected defensive header from Ryan Sessegnon almost gave Salah a tap-in, but Hugo Lloris was alert to the danger.
Van Dijk headed against the top of the Tottenham crossbar from a Trent Alexander-Arnold corner, before Luis Diaz drew a save from Lloris with a fizzing low strike. Pierre-Emile Hojbjerg served a reminder of the visitors' threat when his skidding drive hit the outside of the left post.
Liverpool were full of purpose, swarming and probing early in the second half for the big chance that might bring a breakthrough.
However, they were stunned by Son in the 56th minute, when he slotted past Alisson after Kane's pass to Ryan Sessegnon on the left was followed by a sharp centre to the unmarked South Korean.
Jurgen Klopp threw on Diogo Jota, looking for a spark, and Salah soon had a great chance as he cut inside on his left foot, only for Ben Davies to produce a glorious block.
Diaz hit the equaliser when his 22-yard strike took a massive deflection past Lloris, finding the bottom-left corner, and try as they did, Liverpool could not find a second.