Andre Villas-Boas' visitors secured a comprehensive victory over third-tier opposition at Brunton Park to book their progression into the last 16 of the League Cup
Andre Villas-Boas' men dominated the first half and Clint Dempsey had an effort cleared off the line before defender Jan Vertonghen headed home Gylfi Sigurdsson's cross on 37 minutes for his first Spurs goal.
The hosts missed a couple of chances to equalise and were made to pay when Andros Townsend hammered home an impressive long-range strike shortly after the break before the Icelander struck to seal victory in the closing stages.
Carlisle, who came into the game on the back of four unbeaten games in League One, made one change to their side. Kallum Higginbotham, the forward on loan from Huddersfield, replaced cup-tied Joe Garner.
Tottenham made eight changes from their Premier League victory over QPR. Carlo Cudicini was a surprise choice in goal, meaning that Hugo Lloris missed out on a chance for game-time, while youngsters Adam Smith and Ryan Mason were handed starts.
The match started in a lively fashion, with both sides enjoying half chances before Iago Falque forced a fine save from Mark Gillespie as a chance presented itself after a corner.
Sigurdsson threatened when he found the side netting with a threatening effort on 13 minutes and Townsend also enjoyed a good start to the match. The winger combined with both Dempsey and Sigurdsson to provide Mason a chance but he could only shoot off-target.
Townsend was again involved when he crossed for Dempsey in the 25th minute but the American headed a presentable chance over the crossbar.
The away side were totally dominating proceedings and the ex-Fulham man saw another effort cleared off the line two minutes later after Mason's initial shot was parried by Gillespie.
It was only a matter of time until the first goal arrived for Spurs and it came through Vertonghen. Sigurdsson sent in a delicious cross from the right-hand side and the Belgian defender's looping header beat Gillespie.
The hosts launched an immediate response and squandered two chances to equalise when Matt Robson took too long to pull the trigger inside the box and then Higginbotham shot wide moments later, meaning that the visitors deservedly went in 1-0 ahead at half-time.
Carlisle wasted another good opportunity to equalise three minutes after the restart when Danny Cadamarteri shot wide from 20 yards when he would have been wiser passing to Higginbotham, who was in good space on his left.
That miss would prove costly when Tottenham grabbed an impressive second goal through Townsend on 53 minutes. The 21-year-old picked up possession on the halfway line, cruised past two weak challenges and hammered a shot into the bottom corner from 25 yards.
Mason was involved all night and came close to getting a goal to show for his efforts but his header from Smith's cross was scrambled away by Gillespie.
The youngster had another opportunity to score with another header on 70 minutes, this time from Townsend's delivery but Gillespie tipped his effort onto the crossbar and impressively saved Sigurdsson's attempt from the rebound too.
Cadamarteri forced Cudicini into a routine stop at the other end with 15 minutes to go, as both sides utilised their substitutes in the latter stages.
One of the Spurs replacements, Jonathan Obika, almost made an instant impression when Gillespie cannoned a clearance against the young forward and the keeper was fortunate to see the ball rebound safely into his arms.
A third goal did arrive with just two minutes left on the clock. Another substitute, Kyle Walker, cut in from the left-hand side after being found by Falque and dinked in an inviting cross, which Sigurdsson headed home from close range.