And this was their worst loss in any competition since 1991 after failing to recover from Sterling's fourth-minute opener.
Pep Guardiola had described this match as a "final" for his side given that Chelsea had a week to prepare, while City ground out a 2-0 win at Everton on Wednesday.
Mauricio Pochettino will still have the genius of Son Heung-Min (watch out for this man) and Cristian Eriksen to fall back on, but even he will admit that his opponents have a significantly lesser threat to deal with than before - and a better-than-before chance to win it.More news: Will Smith Makes His Very Blue Debut in Aladdin Trailer
"But absolute credit to them, they have put a winning run together since then, and with City and Liverpool dropping points, we are now looking at a three horse race for the title".
Maddison picked the ball up, ready to take the spot kick, but Puel immediately sent Vardy on in place of Demarai Gray to take the penalty, and Leicester's top scorer saw his powerful effort saved by Hugo Lloris.
Pochettino added Spurs striker Harry Kane, who injured his ankle last month, was making progress but would not return in time for Sunday's game or the Champions League last-16 first leg against Borussia Dortmund on Wednesday.
"I'm more relaxed because we won the game - we got three important points - but so disappointed with the situation. The way we conceded [chances] is more than we usually concede but I think the victory's fair".More news: Mark Lawrenson states his prediction for Man City v Chelsea FC
Leicester have lost four of their last five league games, increasing the pressure on under-fire boss Claude Puel.
Jamie Vardy stepped off the bench to take Leicester's penalty against Tottenham - but his first touch did not go as planned.
"It is so hard to understand why, when we had one week clear to play this game and to schedule it on a different day, and only I am explaining my feelings and how hard it is to prepare a game when you only have today and then you're going to need to play".
It must be said though, that Spurs have been attached to potential interest in a number of players over the past two transfer windows, only to see nobody brought through the doors in London.More news: Grammys Producer Ken Ehrlich Responds to Ariana Grande: "It Was a Surprise"
"Maybe it was not a good thing, but we had a lot of chances, not just with this penalty".