Raheem Sterling’s second-half solo goal means Liverpool go into their Capital One Cup semi-final second leg with Chelsea with the scores level at 1-1, despite dominating at Anfield.
Chelsea took the lead on 18 minutes after Emre Can brought down Eden Hazard in the area, before the Belgian dusted himself off to slot the penalty past compatriot Simon Mignolet.
Steven Gerrard hit the post and Adam Lallana forced a fine save from Courtois as Liverpool desperately searched for a winner to take a lead to Stamford Bridge for the second leg, but the hosts had to settle for a draw.
There were strong appeals for a Liverpool penalty just before half-time, but referee Martin Atkinson waved play on as the ball struck Diego Costa’s hand as he lay on the ground inside the box.
The two sides meet for the return leg at Stamford Bridge on January 27.