Carvalhal was sacked by Wednesday on Christmas Eve after two-and-a-half years in charge and had claimed he would rather the first meeting between the sides had gone straight to penalties than a replay.
However, the Premier League side’s greater reserves proved their worth as both sides again named much-changed sides with survival in their respective leagues top of their priority list.
A Carvalhal double substitution at half-time swung the tie in the hosts’ favour as Jordan Ayew came off the bench to break the deadlock 10 minutes into the second period.
Nathan Dyer then made the game safe 10 minutes from time when he slotted home Tammy Abraham’s pass.
Spurs host Rochdale for the final place in the last eight at Wembley on Wednesday.
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