After Kevin De Bruyne's fifth-minute opener was canceled out by Liverpool forward Diogo Jota eight minutes later, City goalkeeper Ederson slipped as he tried to clear Kyle Walker's back-pass but he recovered just in time.
City did go in at halftime in front after Gabriel Jesus beat the offside trap to get on the end of João Cancelo's cross for his first league goal in 16 matches.
But whatever Jürgen Klopp told his Liverpool players at halftime worked. From the restart, Trent Alexander-Arnold played in Mohamed Salah and the pass was slipped in for Mane to lift a shot over onrushing City goalkeeper Ederson.
City manager Pep Guardiola slumped into his padded seat. By full time — just after City substitute Riyad Mahrez scooped the ball over — there was an embrace with Klopp.
And now on to Wembley on Saturday for the third instalment of hostilities between the teams with a place in the FA Cup on the line. The Premier League and Champions League remain the bigger targets for the greatest rivals of this English era.
RELEGATION SCRAP
It's tight at the bottom, and Norwich is keeping up the fight to avoid the drop after beating relegation-rival Burnley 2-0.
Goals from Pierre Lees-Melou and Teemu Pukki moved the last-place team within seven points of survival, but 17th-place Everton has a far superior goal difference. Burnley is four points behind Everton, while Watford is a further two adrift.
Brentford can be more certain of not being sucked into the relegation fight after beating West Ham 2-0. Bryan Mbeumo and Ivan Toney set each other up for goals for the win that moved Brentford 12 points clear of the relegation zone with six games remaining.
FIRST GOAL
Kiernan Dewsbury-Hall, a 23-year-old Leicester academy graduate, scored his first Premier League goal after assisting Ademola Lookman's opener to clinch a 2-1 win over Crystal Palace. Leicester dislodged Palace from ninth place.