The 50 million-pound ($79 million) Spanish striker scuffed a shot into the Leicester net after 67 minutes to send the Stamford Bridge crowd into raptures and he found the target again with a deft header five minutes from time.
The win continued Chelsea’s revival under caretaker manager Roberto Di Matteo.
Liverpool host Stoke City in the last quarter-final later on Sunday.
Everton drew 1-1 with Sunderland on Saturday and the game between Tottenham Hotspur and Bolton Wanderers was abandoned before halftime after Bolton midfielder Fabrice Muamba collapsed on the pitch. Muamba remained in a critical condition on Sunday.
(For more sports news and updates, follow Ahram Online Sports on Twitter: @AO Sports)