Chelsea launched the post Andre Villas-Boas era in winning fashion as second half goals from Juan Mata and Raul Meireles secured a 2-0 victory at St Andrews on Tuesday night.
Two goals in six minutes approaching the hour mark from Juan Mata and Raul Meireles gave Roberto di Matteo a winning start to his reign as Chelsea's caretaker boss.
The Londoners, held to a 1-1 draw by Blues in the original tie, then had Mata's penalty saved by Blues goalkeeper Colin Doyle.
Blues battled until the end, but Mutch chipped over the bar from Chris Burke's ball while Chelsea keeper Petr Cech stood tall to save from Marlon King.
Chelsea will be at home to Leicester City in next week's quarter-finals.