Manchester City thought they had done it. Thought they had won a stunning Champions League quarterfinal with an even more stunning finish. Raheem Sterling scored in stoppage time to put City ahead of Tottenham 5-4 on aggregate in the second leg. He appeared to have put City in the semifinals.

And then the referee put his finger to his ear, signaling a VAR review.

Moments later, he put his hand in the air.

Offside.

After wild City celebrations – and after Spurs players had crumpled to the Etihad turf, dejected, thinking they had thrown their Champions League dreams away – it’s Tottenham who is heading through to the Champions League semis thanks to video review.

Why VAR ruled City’s goal offside

Had the goal stood, Christian Eriksen would have been the goat. His ill-advised back-pass had trickled through to Sergio Aguero. Aguero had squared to Sterling, who seemingly won the game.

However ... few realized it in real time, but when Eriksen’s back-pass was deflected by Bernardo Silva, Aguero was offside by half a length:

“I’m one of the luckiest guys on the planet,” Eriksen said in a postmatch interview.

It was the most remarkable of emotional swings in such a short period of time. That emotion fueled controversy.

But it was the right call. The deflection, in the eyes of soccer’s laws, is the equivalent of a pass. And when Silva played the ball, Aguero was clearly goal-side of the last Tottenham defender.

This is precisely why VAR was introduced. Hate it or love it, it reversed a critical error.

Spurs, though, are indeed lucky it was introduced in the first place. When UEFA initially decided to adopt the replay review system – which has been used in many top domestic leagues and at the 2018 World Cup – its goal was to implement it next season. That was in September.

But in November, with the 2018-19 competition already underway, UEFA executives decided to push forward the debut date and implement VAR for the knockout stages. And nowhere was that decision more impactful than over 180 minutes at Wembley Stadium and the Etihad.

VAR plays critical role in City-Spurs quarterfinal

Wednesday’s decider was the third massive VAR review of the Manchester City-Tottenham quarterfinal.

In the first leg, replay awarded City a penalty – which Aguero missed – after a handball that had looked innocuous in real time.

Then, in the second leg, Fernando Llorente’s goal – which turned out to be the winner – was the subject of a dramatic review:

The ball appeared to have grazed Llorente’s forearm before ricocheting off his hip and in. But the goal was correctly upheld. Overturning a judgement call requires the recognition of a “clear and obvious error.” With Llorente’s arm tucked into his body, this was not one.

Offside, however, is not a judgement call. It can be tracked, down to the inch, by technology. There is zero doubt Aguero was offside moments before Sterling thought he’d completed his hat trick.

And there is zero doubt Tottenham is moving on to its first-ever Champions League semifinal in dramatic fashion.

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Henry Bushnell is a features writer for Yahoo Sports. Have a tip? Question? Comment? Email him at henrydbushnell@gmail.com, or follow him on Twitter @HenryBushnell, and on Facebook.