Three goals from Jan Vertonghen, Andros Townsend and Gylfi Sigurdsson saw Tottenham book a place in the last 16 of the Capital One Cup where they will now face a trip to Norwich.
Spurs boss Andre Villas-Boas rung the changes from the side that beat QPR at the weekend and handed starts most notably to Michael Dawson and Tom Huddlestone who were both close to moves away in
The deadlock was broken in the 37th minute when Vertonghen headed in Sigurdsson's well-delivered free-kick to give Spurs a 1-0 lead at the break.
And not long after the interval the visitors were two up as Townsend picked up the ball on the half-way line, drove past two defenders before slotting home.
Carlisle played with great spirit in the second half but their fate was sealed in the final minute when Sigurdsson headed home Kyle Walker's cross to secure Tottenham's passage into the next round.
Andre Villas-Boas' side are now unbeaten in six games.
Up next they face a tough away trip to Old Trafford on Saturday.