Liverpool manager Jurgen Klopp missed the game after a suspected positive test for Covid-19 while Chelsea manager Thomas Tuchel dropped £97.5m record signing Romelu Lukaku from his squad after a controversial interview in which he expressed discontent with his current situation.
It looked like Klopp would be the happier of the two bosses when Sadio Mane, fortunate to escape with only a yellow card after flattening Cesar Azpilicueta with a high elbow in the opening seconds, pounced on Trevoh Chalobah's mistake to put Liverpool in front after nine minutes.
Mohamed Salah's moment of individual genius, a feint to fool Marcos Alonso then a perfect near-post finish, put Liverpool in command before Chelsea staged their comeback on the stroke of half-time.
Mateo Kovacic's spectacular volley flew beyond Liverpool keeper Caoimhin Kelleher, in for Alisson who also had a suspected positive test for Covid, after 42 minutes before Christian Pulisic raced clear to equalise in first-half stoppage time.
In a hugely entertaining game, both sides had chances to win in the second half with Chelsea keeper Edouard Mendy saving superbly from Salah and Mane while Kelleher thwarted Pulisic.
A winner could not be found, which leaves Chelsea, in second, 10 points behind City while Liverpool, in third, are 11 adrift of the leaders with a game in hand.