Spurs went into the game after creating a new Premier League record with a 1-0 win against Newcastle last weekend seeing them go 29 matches without a draw.
And, while Leicester enjoyed the better of the first-half play, Davinson Sanchez’s first league goal for Spurs got the hosts’ noses in front at the break.
Jamie Vardy could have levelled with his first touch off the substitutes’ bench but saw his penalty saved, before Christian Eriksen looked to have sealed the points moments later.
However, Vardy made amends for his penalty miss by pulling a goal back to set up a tense final 15 minutes, but Spurs sealed the win in stoppage time when Heung-min Son scored on the counter-attack.
Spurs move within five points of leaders Liverpool, while Leicester are without a win in their last five Premier League games and sit down in 12th place, eight points clear of the relegation places.
Spurs boasted three changes to the side which defeated Newcastle as Fernando Llorente, Oliver Skipp and Danny Rose came into the XI in place of Lucas Moura, Erik Lamela and Toby Alderweireld.
Leicester boss Claude Puel made two changes to his side that was beaten 1-0 by Manchester United last week as Youri Tielemans was handed his debut while Rachid Ghezzal replaced Vardy up front. However, Wilfred Ndidi was later added to the XI when Nampalys Mendy picked up an injury in the warm up.
Spurs started brightly but it was Leicester who created the first chance of note in the eighth minute when Harry Maguire met James Maddison’s free-kick and Hugo Lloris was on hand to tip his header over the top.
A minute later Harvey Barnes dragged his shot wide when he should have done a lot better as the hosts were again fortunate not to fall behind.
Son was harshly booked for simulation on 16 minutes when he went down in the area under a challenge from Maguire, despite there being clear contact on the South Korean.
Spurs pressed again minutes later with Rose being teed up by Llorente only for Kasper Schmeichel to push away his effort with Llorente then offside when going for the rebound.
Leicester came back again on 21 minutes with Tielemans providing a good pass for Barnes down the left and his pull-back picked out Maddison who curled his attempt just wide.
The visitors continued to look the more likely with Ben Chilwell picking out Ndidi at the near post on the half-hour, but his flick dropped just wide, although the offside flag was harshly raised against him.
On 31 minutes Barnes was guilty of another missed opportunity when he dragged his effort wide of Lloris’ right-hand post following good work by Chilwell.
However, it was Spurs who broke the deadlock against the run of play on 33 minutes when Colombian defender, Sanchez, dived to head in Eriksen’s cross which was swung in from the right channel.
Leicester almost levelled right on half-time when Tielemans' cross from the right caught out Lloris who managed to divert the ball behind before it could creep inside his near post.
Spurs had the first chance after the break when Llorente couldn’t divert his header from a Kieran Trippier cross on target, before Leicester had several chances to get back on level terms.
Demarai Gray had a header and a shot saved by Lloris, who then thwarted Chilwell who had an attempt from around 30 yards.
Leicester were then given a golden opportunity to level matters when Maddison went down under a challenge from Jan Vertonghen in the area and referee Michael Oliver awarded a penalty.
Vardy stepped off the bench in place of Gray, but watched as Lloris dived to his right to tip his subsequent spot-kick wide of the goal on the hour mark.
The Foxes were made to pay for that miss when Spurs doubled their lead three minutes later as Llorente’s lay-off fell to Eriksen just outside of the area and he curled a wonderful strike inside Schmeichel’s post.
Leicester should have been back in the game on 66 minutes when Barnes was played through into the area by Vardy but saw his effort well saved by the legs of Lloris.
The visitors got the goal their play warranted on 76 minutes when Ricardo Pereira got free down the right and his low cross into the middle was touched home from close range by Vardy.
On 83 minutes Pereira again got clear down the right but this time he cut inside onto his left foot and dragged his effort just wide of the near post.
The points were sealed in injury time when Moussa Sissoko sent Son away for a clear run at goal and, while the Foxes defence gave chase, he kept his cool to guide a low effort beyond Schmeichel.