Pep Guardiola's men dominated the first period, with the best chance of the first 45 minutes falling to the impressive Foden after a scintillating run from Bernardo Silva, but the Englishman's effort was well saved by Alisson.
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De Bruyne also came close, but his diving header from ten yards went over the crossbar.
The hosts emerged from the interval with a spring in their step and took the lead through Sadio Mane, who calmly converted from Mohamed Salah's pass.
City bounced back ten minutes later and equalised through the electric Foden, who blasted into the far corner from Jesus' pass.
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Seven minutes later, City were pegged back again, this time through Salah, who danced into the box and struck beyond the sprawling Ederson.
Guardiola's men regrouped again and levelled with nine minutes remaining through De Bruyne, whose powerful shot deflected off Joel Matip and past Alisson.
Jurgen Klopp's side could have snatched all three points at the end, but Rodri's sensational last-ditch block denied Fabinho a certain goal with the goal gaping.
The breathtaking draw takes City into third place in the Premier League - you can view the best images from the pulsating clash via the gallery below.