Spurs responded to Arsenal and Chelsea's victories from earlier today to regain third in the Premier League table with their eighth away win from 10 this season.
Mauricio Pochettino's side will hope to take this momentum into Tuesday's crunch Champions League showdown with Barcelona where only a win is likely to be enough to keep them in the competition.
There were flashes of brilliance from Tottenham's forward players, with Lucas Moura showing exemplary control to bring down Eric Dier's pass over the top, but he could not square to the unmarked Alli in the six-yard box.
Alli and Moura did combine on 29 minutes to create an opening for the England midfielder, whose hesitance to get a shot away on his weaker left foot allowed Wes Morgan to get a block in.
The Leicester skipper was on hand to thwart Alli again on the stroke of half time when his last-ditch slide tackle pinched the ball from the Spurs man as he prepared to shoot from 10 yards out.
That intervention looked to have earned the Foxes half-time parity until Son came up with a moment of magic 90 seconds later, drifting infield from the outside right of the box and whipping a shot beyond Kasper Schmeichel.
Son's effort was the only shot on target during the first half, but the second period was a little more open as Leicester came out in search of an equaliser. However, they struggled to create clear-cut chances and their greater ambition mostly favoured Spurs.
Demarai Gray did work Hugo Lloris with a left-footed shot on 53 minutes, but he failed to generate the bend or power that Son had with his similar first-half strike, and it was fairly easy pickings for the Tottenham goalkeeper.
Spurs doubled their lead on 58 minutes through Alli's 50th goal for the club, a back-post header from Son's cross after Ben Davies had split the Leicester lines with a fine pass, although the Foxes may claim the goalscorer was offside.
Kane and Eriksen did come off the bench to allow Son and Lucas a rest with Barcelona in mind, but Tottenham's third substitution may be a concern for Pochettino with Serge Aurier forced off with an injury, and fellow right-back Kieran Trippier already sidelined.
Leicester did not offer much suggestion of a comeback and only worked Lloris again when Rachid Ghezzal came off the bench to call the Frenchman into action, firstly with a right-footed curler and then a left-footed half volley.
Otherwise the Foxes failed to make the most of their territory as Toby Alderweireld and Jan Vertonghen, who kept a clean sheet on their first Premier League start together for two months, held firm under a series of crosses and corners.
This result brings to an end Leicester's six-match unbeaten run in the Premier League, and takes Spurs to within six points of the top of the table which may give them some belief ahead of their unenviable European task this week.
LEICESTER (4-3-3): Schmeichel; Pereira, Morgan, Evans, Chilwell; Mendy (Okazaki 79'), Ndidi, Iborra (Albrighton 56'); Maddison, Gray, Iheanacho (Ghezzal 56')
SPURS (3-4-1-2): Lloris; Aurier (Walker-Peters 78'), Alderweireld, Dier, Vertonghen, Davies; Sissoko, Winks; Dele; Son (Kane 74'), Lucas (Eriksen 67')