With goals from Sadio Mane and Mohamed Salah, the Reds raced into a two-goal lead, demonstrating a lethal edge in the Chelsea box.
Before halftime, though, the Blues came back with a thunderbolt from Mateo Kovacic and a pinpoint effort from Christian Pulisic.
Both teams pushed hard in the second half, but none could find a way to win.
Chelsea is still in second place, while Liverpool is in third, both teams trailing Manchester City at the top of the standings.
Chelsea will face Tottenham Hotspur in the EFL Cup semi-finals at Stamford Bridge on Wednesday.
Liverpool is also in EFL Cup action on Thursday, when they face Arsenal at the Emirates Stadium in a last-four match.