City dominated the first half but could not find the finishing touch and they were made to pay when Sadio Mane put Liverpool into the lead just before the hour mark.
Phil Foden equalised 10 minutes later before Mohamed Salah scored a brilliant individual goal to put the hosts back in front with 14 minutes remaining.
But Kevin De Bruyne’s deflected strike brought the scores level again and both sides missed chances to win it.
The result leaves Liverpool one point behind Chelsea at the top of the Premier League table, with City a further point behind in third.
Tottenham got back to winning ways with an important 2-1 victory over Aston Villa.
Spurs had lost their last three Premier League games by an aggregate of 9-1 and the pressure was beginning to grow on Nuno Espirito Santo following a dismal performance in last week’s north London derby defeat by Arsenal.
But Pierre-Emile Hojbjerg’s strike and an own goal by Matt Targett got the job done as Spurs go into the international break on a positive note.
Villa were outplayed but found themselves level with 22 minutes remaining as Ollie Watkins scored his first goal of the season, only for the hosts to regain their lead three minutes later.
Jeffrey Schlupp came off the bench to earn Crystal Palace a share of the spoils against former club Leicester – who let a two-goal lead slip at Selhurst Park.
The Foxes looked on course for a first Premier League win since August as birthday boy Kelechi Iheanacho and Jamie Vardy capitalised on defensive errors to put them two goals up at the interval.
But Palace rallied as substitute Michael Olise scored his first goal for the club before Schlupp struck as Patrick Vieira’s side claimed a battling 2-2 draw.
Yoane Wissa thumped home a stoppage-time winner as Brentford floored West Ham 2-1 at the London Stadium.
The Bees leapfrogged their opponents in the Premier League table courtesy of DR Congo forward Wissa’s last-gasp strike.
Jarrod Bowen thought he had scrambled the Hammers a draw with his first goal in 15 Premier League games 10 minutes from time, but replacement Wissa blasted into the net after the hosts failed to clear from a Mathias Jensen free-kick.
Bowen’s low finish cancelled out Bryan Mbeumo’s opener for the Bees and almost grabbed West Ham a point.
REUTERS