That Man City game was probably the single most "against the run of play" victory of a multi-goal margin I've ever seen. And I'm not just saying that to be hyperbolic. The fact that Man City had a full 66% of the possession is actually the smallest discrepancy and least surprising stat (I've never been a fan of the idea that possession stats tell you who "should" have won a game).
Man City missed a penalty and should've had another; they took 14 shots from which they missed the target entirely for genuine open goals and hit the woodwork more than once; some of their misses were absolutely farcical and left me with my mouth open, muttering "how the feck?" under my breath; and they played a third of the match with ten men because of a somewhat dubious red card for Zinchenko, and only after that did Spurs manage to get even a few vague opportunities to shoot. Before the red card, it was looking like Spurs could play forever and never get a sighter (unlike City, who looked like they could play forever and never find a way to not feck it up in spectacular fashion).
The first Spurs goal from their new lad was class but it was basically their first shot on or off-target after 62 minutes(!!); they went on to have another two shots in total; Son's shot-turned-goal was hit directly at the keeper and was nailed on to be saved until it took a horrendous deflection off a City player and into the opposite side of the goal -- the role of the deflection was so extreme that the effort was functionally an own goal because it was getting saved otherwise (and if you look at Son's kerfuffle of a first touch, he was lucky to retain possession long enough to get any shot away).
Words can't do justice to how unbalanced the game actually was. The stats can give you an idea and the official highlights on YouTube offer a decent reflection of the respective (mis)fortunes of the day, but only watching the match itself or extended highlights that include all of City's chances (which would then include no more Spurs chances than the official version because there weren't any) can really tell the whole story.
Surprisingly, the Southampton win wasn't vastly less fortunate: Spurs required an OG and a debatable last gasp penalty to avoid losing the game, whereas Southampton had to be rather unlucky (featuring the woodwork again) for their part in losing. Southampton were fantastic at times, especially the Redmond->Ings move[1], and I felt like they would've been excellent value for a win.
The updated record without Kane over 21 games is W7 D5 L9. Still a long way to go but they're at least out of relegation form without him. Now it's just a solidly bottom-half track record.
[1] Could those two be late bloomers, potentially of value to England? I cautiously rated both of them as England youth players but they fell off hard. I'm always careful never to judge over a small sample size to avoid the recency bias that afflicts football discourse like a cancer. It's why I wasn't on the "Salah is the best player in the PL and will aim for 30+ every season" train after his first, probabilistically unlikely, season at Liverpool; or the "Sterling has overtaken Kane as England's best attacker and player" train from earlier in the season (I notice that thread hasn't been bumped lately..); or the "Son has overtaken Kane as Spurs' best attacker and player" train from parts of last year. I find that you avoid looking foolish most of the time if you teach yourself some basic statistical mathematics and both formal and informal logic -- and, failing that, just being aware of and trying to avoid as many cognitive biases as possible.