Having drawn 2-2 in the original tie and with Leicester winning the Barclays Premier League meeting in north London last week, Spurs succeeded in the final part of the 10-day trilogy courtesy of goals from Son Heung-min and Nacer Chadli at the King Power Stadium - the scene of a 1-1 draw in the league in August.
Even the introduction of Jamie Vardy from the bench shortly after Chadli’s strike midway through the second half could not rescue Claudio Ranieri’s side.
In the greater scheme of things the Italian may not be too upset by Leicester’s exit, although he would be unlikely to admit it.
It is reasonable to argue that defeat in last night’s third-round replay may benefit Ranieri and his small squad as they look to maintain their surprise pursuit of the Premier League title.
For Tottenham, who must also harbour ambitions of becoming champions, it means another game in an already busy schedule. Mauricio Pochettino’s team will travel to League One strugglers Colchester in the next round at the end of the month.
Both managers made eight changes from the sides they sent out in the Premier League at the weekend. Leicester boss Ranieri initially swapped nine players but Ritchie De Laet was injured during the warm up so Danny Simpson kept his place. Kasper Schmeichel and Danny Drinkwater also remained.
Tottenham boss Pochettino retained Eric Dier, Erik Lamela and Christian Eriksen, with the latter two allowing Spurs to assume a measure of control in midfield and look the more fluent team early on.
Eriksen had the first chance of the match after 14 minutes when Son did well to spot him with a cut back. The Dane tried to guide his shot into the bottom corner of the net with his instep but his effort went harmlessly wide.
Young full-back Ben Chilwell and recent signing Damarai Gray, both making their home debuts, looked a threat down the left but Leicester largely struggled to create opportunities.
Gokhan Inler took a free-kick, won via the invention of academy product Chilwell, but it was easily fielded by Michel Vorm in the Tottenham goal.
Son provided the one real moment of class in the first half after 39 minutes and it separated the teams at the break.
The South Korean collected a pass from Tom Carroll towards the right-hand side of the penalty area and unleashed an unstoppable shot which beat Schmeichel at the near post.
Gray forced Vorm to palm away his curling effort at the start of the second half but Tottenham still looked the most threatening and substitute Harry Kane, a former Leicester loanee, twice came close to making it 2-0 but Schmeichel got down well and got a strong wrist behind each shot.
Shortly afterwards though, the second goal did arrive. Son slid a nicely-weighted pass into the path of Chadli who slotted his shot beneath the goalkeeper in the 66th minute.
Ranierii introduced Vardy, but to no avail. Fellow sub Marc Albrighton nearly pulled a goal back in the final minute but Vorm somehow kept out his volley.
Schmeichel, Simpson (Albrighton - 63’ Booked ), Wasilewski, Benalouane, Chilwell, King, Inler, Drinkwater (Okazaki - 45’ ), Dyer (Vardy - 74’), Ulloa, Gray.
Vorm, Walker, Dier, Wimmer, Davies, Carroll, Bentaleb, Lamela (Kane - 60’ ), Eriksen, Chadli (Onomah - 73’ ), Son Heung-min (Alli - 84’ ).