Pep Guardiola's men began with a spring in their step, immediately pinning the Tottenham team deep into their own half whilst spraying the ball around confidently.
The heavy pressure almost paid off after Kevin De Bruyne's quick throw released Phil Foden, who pulled the ball back for Raheem Sterling but his goal-bound effort was blocked well by Eric Dier, before the winger came close again, dinking the ball across goal but just off target.
The Spurs goal was living a charmed life and the London club escaped again, as Foden's powerful shot from close-range was deflected spectacularly onto the post by Toby Alderweireld just before the half-hour mark.
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The pressure was constant and Riyad Mahrez was next to go close, cutting inside onto his left foot and fizzing a shot just wide of Hugo Lloris' far post.
The Frenchman was then called into action just before the interval, sprawling to palm away Cancelo's accurate strike.
Tottenham emerged from the interval with attacking intent and immediately forced Zack Steffen into a superb save from Giovani Lo Celso's curling strike which was destined for the bottom corner.
After that save, normal service was resumed as City dominated the ball and the chances for the entirety of the second period.
Mahrez came closest to breaking the deadlock with a wonderful solo run, weaving past players before unleashing a powerful strike towards the bottom corner, but once again, Lloris got down well to palm away.
With eight minutes remaining, City made the all-important breakthrough.
De Bruyne's free-kick into the box was met commandingly by Laporte, who thundered the ball into the side netting beyond a helpless Lloris.
Mahrez had the ball in the net late on but it was ruled out for Foden being offside in the build-up, as City remained firm to claim a record-equalling fourth successive League Cup title!
View the best images from the encounter via our gallery below...