But Tottenham hit back inside three minutes as Erik Lamela beat slow-to-react City keeper Ederson from the edge of the area. The scenes at the end were reminiscent of the Champions League clash between the sides at the same venue last season, when Spurs also came out on top.
City's 2-2 draw with Tottenham proved to be a real roller-coaster ride of emotions for the Etihad supporters.
City will have a bitter taste in their mouth, especially after the late VAR drama against Spurs in the UEFA Champions League quarterfinal second leg last season.
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Having only been introduced into the Premier League this season, it has already caused controversy, after a separate decision went against City last week. But if anyone needed proof that Guardiola's team are better with the Belgian in it, he delivered it here.
The hosts thought that had arrived in injury time when Sterling struck, prompting wild celebrations from City boss Pep Guardiola.
It is only Matchweek 2, but few Premier League days will match this.
Jesus replaced Aguero and headed wide as City pushed for a victor but the real drama came in injury time as the Brazilian struck but the goal was disallowed after a long review. Helped keep Harry Kane quiet and the Spurs striker barely had a kick.
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City appeared to step it up after the break with De Bruyne shooting narrowly wide, Aguero firing over on the turn and Bernardo Silva testing Hugo Lloris.
MF Kevin De Bruyne, 8 - Two attractive crosses from the right created two goals in the first half. That result should look better and better as the season progresses. Tottenham deserve credit for their clinical finishing, but they didn't create almost enough chances during the match.
FW Raheem Sterling, 7 - After scoring a hat-trick against West Ham, his stooping header at the back post put City a goal up.
"It's always more hard in a big game but we nearly totally dominated them".
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Once taken off for Gabriel Jesus, who saw a very late victor denied by the video assistant referee (VAR), the club's record goalscorer looked nonplussed and made his feelings known to Guardiola who in turn give back as good as he got.