Kane, who has been strongly linked with a move to City, was reportedly deemed not sharp enough after only recently returning to training, but Spurs adapted well to the situation after a shaky start against a visiting side who handed a debut to British record signing Jack Grealish.
Spurs' reliance on counter-attacking football may have initially frustrated sections of the crowd at Tottenham Hotspur stadium, but it looked like the most realistic way of hurting City in the first half.
And that tactic bore fruit in the 55th minute, with Son rounding off a flowing move with a fine finish that even Kane would have been proud of, denying City the chance to set a new record of 11 successive opening-day wins in the Premier League.
Spurs looked to be in for a long day after a difficult opening that Pep Guardiola's men dominated, with Joao Cancelo and Riyad Mahrez both having presentable chances fall to them, but they weathered the early storm.
The hosts were set up to threaten on the counter and several times they looked bright bursting forward, though uncharacteristically meek play from Son twice saw encouraging moves peter out.
The South Korean looked a little more like his usual self just before the interval, though, seeing a curling effort deflected agonisingly wide by Cancelo after a rapid break.
Spurs began the second period much sharper than the first. Within five minutes of the restart, Ruben Dias had to be alert to prevent Son from having a tap-in and then Lucas Moura shot wide from 20 yards.
Son soon found his range, however, tucking a lovely effort inside the left-hand post from just outside the box after Nathan Ake failed to engage him at the end of a blistering break, setting up a fourth straight win for Spurs over City on home soil.
Spurs were pressed into defensive action in the latter stages, with Hugo Lloris becoming increasingly busy, but they held on to secure only their fifth win in 13 league games without Kane since the start of 2019-20.
What does it mean? Wasteful City need options in attack
While the £100million signing of Grealish will surely be worthy, it looks as though City are going to need more if they are to take themselves to the next level, with their inability to find the net despite their expected goals being almost double that of Spurs (1.0 v 1.8).
While Ferran Torres has occasionally done a job leading the line for City, he is not a central striker and Gabriel Jesus does not seem to have convinced Guardiola in that position either, otherwise he would surely have started.
Kane is the obvious option – perhaps after seeing this match play out, Guardiola will have renewed desire to get him in as soon as possible.
Son shines without Kane
In the past few years, a lot of the praise that has come Son's way has often related to his relationship with Kane, rather than the merits of his own quality. Although he seemed strangely subdued early on, he soon got himself on the front foot and proved a real nuisance to City, his five shots more than anyone else on the pitch, and one of those was the excellent goal.
Mendy makes a meal of defensive work
While there were a few situations early on where Benjamin Mendy's ability in attack looked useful, defensively he appeared a weak link throughout. He gifted possession back to Spurs in dangerous positions a couple of times, and was nowhere to be seen for Son's goal on the break.
Spurs go to Pacos Ferreira for the first leg of their Conference League qualifier on Thursday before Nuno reunites with Wolves at Molineux next Sunday. City host promoted Norwich City in six days' time.