Goals from Simonas Stankevicius, Danny Drinkwater and a penalty from Jak McCourt secured the triumph for Steve Beaglehole’s side, while Kenny McEvoy was on target for the visitors.
The fixture provided suitable game time for a number of first-teamers, with Ben Hamer, Marc Albrighton, Drinkwater and Anthony Knockaert all in action, while youngsters Ben Chilwell, Harry Panayiotou, Layton Ndukwu and Jack Barmby were all away on international duty.
The Foxes occupied fifth position in the league going into the tie and knew they could move within two points of table-topping Manchester United with a victory, while Tottenham sat one place and two points above Leicester.
Plenty of early possession from City saw Drinkwater register the first effort of the game, hammering a fearsome half-volley just inches wide of the mark on 10 minutes.
The lively McEvoy raced down the right flank three minutes later, only for defender Elliott Moore to cut out his dangerous cross to the edge of the box.
Hamer was forced into his first save of the game on 19 minutes, getting down well to his left to deny Anton Walkes from distance.
McCourt then saw his placed effort deflected agonisingly wide by Christian Maghoma before Albrighton tired his luck from range, driving a shot just past Luke McGee’s upright.
City’s best chance of the first half came on 33 minutes. Joe Dodoo plucked Kieran Kennedy’s pin-point pass out of the air and raced down the wing. Maghoma then headed the wideman’s cross straight to the feet of McCourt, who rattled Tottenham’s post from 25 yards.
Lithuanian international Stankevicius mustered up the final opportunity of the first half, producing a fine turn on the edge of the area, only to see his strike blocked by the defiant Maghoma – nothing to separate the two sides at the break.
It took just one minute of the second half for City to break the deadlock. Knockaert’s cross from the left flank found Stankevicius, who headed in at the front post to give his side the lead.
It then took a neat stop from Hamer to keep the scores level on 53 minutes as the shot-stopper saved well with his feet from Daniel Akindayini’s low drive.
But a lightning break from Leicester saw Drinkwater double his side’s lead. Albrighton flew down the right wing and delivered to the former Manchester United midfielder, who slotted in past McGee on the hour mark.
Stankevicius looked for his second of the game on 69 minutes with a header that flew over the bar, but it was Tottenham who would next find the back of the net.
Winger McEvoy converted substitute Ismail Azzoui’s cross deep in the Leicester box to pull one back for the visitors with 16 minutes to play.
Hamer did well to stop Filip Lesniak’s hit from distance, but City rallied and scored their third goal from the penalty spot.
Captain James Pearson was brought down in the box before McCourt dispatched from 12 yards to seal the three points for his side in injury time.
City next face Manchester City at their Academy Stadium on Sunday 5 April before a home tie against Liverpool on Monday 13 April.
CITY: Hamer, Pearson (c), Sesay, McCourt, Kennedy (Fox 46 (Scott 74)), Moore, Albrighton, Drinkwater, Stankevicius, Knockaert (Kipre 81), Dodoo
SUBS NOT USED: Smith, King
GOALS: Stankevicius 47, Drinkwater 60, McCourt pen 90
TOTTENHAM: McGee, McQueen, Ogilvie, Lesniak, Maghoma, Carter-Vickers (c), McEvoy, Walkes (Azzaoui 71), Akindayini, Harrison, Miller (Goddard 81)
SUBS NOT USED: Miles, Loft
GOAL: McEvoy 74
REFEREE: Daniel Meeson