A fine second half strike from Raheem Sterling gave Liverpool a fully deserved goal in this exciting Anfield cup tie.
The reds travel to Stamford Bridge next week for the second leg with hopes of another Wembley trip still alive. The reds made one change from the weekend's win away at Villa - Steven Gerrard replaced goalscorer Fabio Borini.
Liverpool had the majority of the chances, and with a striker of the calibre of Daniel Sturridge maybe would have had more to show for their efforts.
As it was Chelsea scored first against the run of play when Eden Hazard won and then dispatched the penalty.
It arrived in the 18th minute when Emre Can blocked Hazard who appeared to already be on his way down.
The reds responded well to this setback which was against the run of play. Coutinho was vibrant, Sterling was working hard as the reds main striker - Lucas and Henderson were supporting the play well from their midfield berth.
There was some controversy just before half time when Diego Costa appeared to stop the ball with his hand. The referee waved away the penalty appeals.
Second half and the reds continued to show their improving confidence - pressure mounted and then in the 59th minute Liverpool broke through. Despite all the possession in the Chelsea final third this goal came from a quick release from the centre of the pitch. Henderson played the ball forward to Sterling who turned and burned Cahill for pace before firing a left footed shot into the bottom corner of the Kop goal.
Liverpool fans could sense a winner - Gerrard hit the post, his replacement Lallana fired a powerful shot that was tipped around the post, Henderson and Sterling had two quick succession shots that were denied by Courtois (who went on to receive the Man of the Match award).
The reds couldn't quite get the extra goal which they possibly deserved. Chelsea now have the slender advantage of an away goal - which will only count if required after extra time next week.