Sterling thought he had completed a stunning hat-trick in the dying moments of a pulsating Champions League quarter-final but VAR intervened and Spurs went through to the semi-finals despite a 4-3 defeat on the night.
Sergio Aguero was adjudged to have strayed offside in the build-up, deflating City and meaning that Spurs would prevail with the score 4-4 on aggregate.
It was an incredible ending to a thrilling contest, which had seen both sides lead.
Sterling and Son Heung-min both struck twice in the first half, with Bernardo Silva’s deflected effort giving the hosts the lead.
An Aguero strike then put City in control of the tie but a bundled Fernando Llorente goal proved decisive for Spurs.
The tone for a frantic night was set as Sterling curled home his first after just four minutes. Kevin De Bruyne was twice involved in a quick break before Sterling cut inside Kieran Trippier and bent a low shot past Hugo Lloris from just inside the area.
That had the stadium rocking with the supporters who seemed to have responded to Pep Guardiola’s rallying call at their loudest.
Yet they were silenced within moments as Spurs responded in stunning style with Son grabbing two quickfire goals.
City contributed to their own downfall with Aymeric Laporte twice giving the ball away. The first time he failed to cut out a Dele Alli pass into the area and Son blasted a shot underneath Ederson.
The second occasion he was further upfield but Spurs quickly broke with Christian Eriksen feeding Son and the Korean curling a superb shot into the top corner.
Remarkably just seven minutes had elapsed but within another four the score was 2-2 as City roared back with Bernardo Silva’s shot deflected in by Danny Rose.
Bernardo Silva was then involved in the move that saw City regain the lead, releasing De Bruyne with a backheel. De Bruyne then picked out Sterling unmarked at the far post with a trademark low cross and the England forward tapped home his 23rd City goal of the season.
That put City back ahead on the night but with them still trailing on away goals they continued to force the pace and the game remained open.
Aguero had a shot blocked before Son beat Kyle Walker at the other end and curled another shot just wide.
De Bruyne scuffed a shot at Lloris and missed the target with a free-kick. The second half started with Lloris denying Sterling and De Bruyne with good saves. Fernando Llorente tested Ederson with a header but the momentum was with City.
The hosts claimed the goal that put them ahead in the tie just before the hour as De Bruyne released Aguero with a sublime throughball. Showing the composure for which he is famed, the Argentinian blasted a ferocious shot past Lloris from a tight angle.
Having gained the initiative in the tie, Guardiola, pictured, tried to protect it by sending on Fernandinho but his plans were soon torn up as Llorente bundled in a controversial effort from a corner after 73 minutes. Play was held up for a VAR referral as the ball appeared to brush the Spaniard’s arm before bouncing in off his hip but he was eventually given the benefit of the doubt. City needed a late response and they thought they had found it as Sterling showed great footwork in the box before poking past Lloris, but VAR saved Spurs.