Mohamed Salah was given a sight at goal after 12 minutes, but the Egyptian failed to hit the target from the edge of the box.
Chelsea had a big chance to break the deadlock on 23 minutes when David Luiz picked out Willian with a superb pass, but Reds goalkeeper Alisson Becker rushed off his line to deny his Brazil teammate.
Two minutes later, the Blues were ahead as Eden Hazard netted for the second straight game against Liverpool with a composed finish from close range.
The Reds nearly hit back in the 32nd minute when Salah rounded Kepa Arrizabalaga but Antonio Rudiger got back in time to clear the effort off the line.
Hazard should have doubled the Blues' lead after the hour mark when he raced clear on goal, but the Belgian failed to slot past Alisson Becker in the box.
Jurgen Klopp threw on Xherdan Shaqiri for Salah, while the Blues introduced Alvaro Morata and Victor Moses for the final 20 minutes.
However, it was another substitute, Daniel Sturridge, who made the difference by finding the equaliser with a stunning curling effort from distance in the 88th minute.
In the end, 1-1 was how the score remains as both sides retain their unbeaten status in the league this season.