City have now tied Liverpool for most men's League Cup titles, with both sides winning eight each.
In a surprise to many, Harry Kane was named in the starting team despite carrying an injury. However, there was little for him to do in the first half as City dominated with Spurs struggling to get a hold of the ball.
Moments later Raheem Sterling saw his shot fly just wide and the half ended with both sides level.
Spurs started the second half brighter, with Giovani Lo Celso forcing Zack Steffen into a rare but excellent save two minutes in. It was a powerful performance from the United States men's national team player who started ahead of No. 1 pick Ederson.
At other end of the pitch, Lloris was forced into a number of good saves as City continued to hammer his goal, including a powerful shot from Riyad Mahrez on 73 minutes.
However, 10 minutes later Laporte headed past Lloris from Kevin De Bruyne's free kick.
The loss continues Spurs' longest trophy drought since 1951. Their last title was the League Cup in 2007-08.
"It was a tough game. We knew it was going to be tough. We kept dominating, we kept passing the ball and I think we deserved to win today," Mahrez said after the game.
"You are always scared because it is a good team but we are confident in our game. We are very happy. You have to win whether you play good or not -- today I think we played good and won."