Vertonghen capped another outstanding display, this time from left-back, by heading home the key first goal from Sigurdsson's perfectly-flighted free-kick in the 37th minute.
Townsend, electric at times, lashed home the goal of the game from 25 yards eight minutes into the second half and Sigurdsson completed a job well done with a header from Kyle Walker's cross in the final minute.
Andre Villas-Boas made eight changes to the team that started against QPR on Sunday.
Most notably, there were first starts for Academy graduates Ryan Mason and Adam Smith and first starts of the campaign for Carlo Cudicini, Michael Dawson, Tom Huddlestone, Yago Falque and Townsend.
The home side set out to stop us playing out from the back with Danny Cadamarteri and Kallum Higginbotham working tirelessly to close us down.
That hard work paid off to a certain extent in the first half as we struggled to find a consistent rhythm to our play, but we still created chances.
Falque shot straight at home goalkeeper Mark Gillespie in the fifth minute, Townsend fired wide, Gillespie produced a fine save to tip over Falque's piledriver from 20 yards and Gylfi Sigurdsson missed the target from the left angle all inside the first 11 minutes.
The next chance arrived on 25 minutes when Clint Dempsey headed over Townsend's cross and three minutes later, the US international was denied by a goal-line clearance from Peter Murphy after Mason bravely went in 50-50 with Gillespie.
The first goal was always going to be crucial and it arrived in the 37th minute. Sigurdsson curled in a free-kick from the right and Vertonghen was there to head home from close range.
Carlisle had a chance to respond immediately and it took two fine blocks to deny them, Huddlestone from Higginbotham and then Dawson flicked over Cadamarteri's follow up.
The second half started relatively quietly until Townsend lit up a packed Brunton Park on 53 minutes.
Picking up the ball on halfway, he turned away from his man before charging forward, cutting across James Berrett before drilling low into the corner from 25 yards.
The home team made three changes on the hour but were now struggling to make any impact going forward as we took control.
Gillespie produced three top-drawer saves to keep the scoreline at 2-0. Mason must have thought he'd scored when he powered a header in from Smith's cross, only for the goalkeeper to get down to his left and hold on at full stretch.
He then topped that with a double save on 69 minutes, initally clawing out Mason's header from Townsend's cross and then blocking Sigurdsson's follow up.
Cadamarteri and substitute Liam Noble fired wide from distance as Carlisle pushed on again, before Jonathan Obika came on for his first appearance since 2008-09, our third substitute following the introductions of Kyle Walker and Tom Carroll.
The next chance - and Carlisle's best - fell to substitute Mark Beck, who headed straight at Cudicini.
We had the final word though in the 89th minute. Falque played a fine pass inside full-back Frank Simek for Walker and he took his time before clipping the ball in for Sigurdsson to plant his header past Gillespie.
Carlisle (4-4-2): Gillespie; Simek, Livesey, Murphy, Chantler; McGovern (Symington, 61), Thirlwell (Noble, 61), Berrett, Robson; Higginbotham (Beck, 61), Cadamarteri. Unused subs: Collin, Madden, Edwards, Potts.
Spurs (4-2-3-1): Cudicini; Smith, Caulker, Dawson, Vertonghen (Walker, 65); Huddlestone, Mason (Carroll, 71); Falque, Sigurdsson, Townsend; Dempsey (Obika, 76). Unused subs: Gomes, Lennon, Sandro, Defoe.
Goals: Spurs - Vertonghen (37), Townsend (53), Sigurdsson (89).
Referee: Mr K Friend.