Sterling was taken off shortly afterward, and Watford substitute Gerard Deulofeu pulled a goal back for the visitors just 17 seconds after going on, scoring with his first touch after Troy Deeney flicked a long ball into the box.
The game appeared to be over and Pep Guardiola opted to withdraw his hat-trick hero, but Gracia also decided to make alterations and it led to his side reducing the deficit.
Once again, there was confusion about the current offside law and its interpretation with Watford players incensed - Sterling appeared to be in an offside position when played in by Sergio Aguero and the assistant referee had raised his flag.
England captain Kane's first-half milestone was eclipsed as third-placed Spurs squandered a lead in a game they were dominating, prompting criticism of his players by manager Mauricio Pochettino.
Once referee Paul Tierney had discussed the decision, including Janmaat's intervention, with his assistant, he eventually awarded the goal - and City went onto score two more in a 3-1 win.
But after such a hard opening period, no-one would have expected that the game would have been settled decisively in City's favour in the opening quarter of an hour after the break.
"I'm not too much concerned or anxious about what people say if we win the title just because what happens now with UEFA". Some clubs did not accept it. I am a little bit anxious about this change from the first half to the second half - it's only one thing, it's mental.
"Hopefully next season, like in Europe, they can accept that we install VAR in this situation and it will be fair. In my opinion, it is clear".
Watford goalkeeper Ben Foster posted on Twitter to mock the decision to award Sterling's goal, while his boss Javi Gracia was in tongue-biting mode in his own post-match interview. The third was more impressive as Sterling collected a pass from Silva and went past two defenders before slotting the ball home. "[Sterling's] position and influence, I think is clear". The three goals were fantastic but he can do better.
As if to offer Liverpool a glimpse of what might have been, Gracia sent on Deeney and Deulofeu in a double substitution and it took them just a matter of seconds to combine for a Watford goal.