With the game goalless at the start of the second half, Sterling was challenged by Daryl Janmaat as he ran on to Sergio Aguero’s flick and the ball cannoned off him and into the net.
Sterling was clearly offside when Aguero chested the ball into his path and the lineman’s flag went up. But, after a long discussion with his fellow official, referee Paul Tierney overruled his decision, to the disbelief of the Hornets players.
There was no disputing the legality of Sterling’s second goal, which came only four minutes later when he tapped in Riyad Mahrez’s cross at the far post after a flowing City move.
And, just before the hour mark, the 24-year-old England forward made it 3-0, running on to a David Silva pass and cutting past two defenders before slotting home his 18th goal of the season.
Watford, who had made seven changes ahead of their FA Cup quarter-final with Crystal Palace next weekend, belatedly threw on Troy Deeney and Gerard Deulofeu – two of those to be left out.
The pair combined seconds later to pull a goal back with their first touches when Deeney flicked on a long ball for Deulofeu to fire home with his side’s first shot, after 66 minutes.
It proved to be only a consolation rather than the start of an unlikely comeback, with City comfortably holding on to clinch their sixth successive league win.
Their four-point lead is their biggest advantage at the top since 4 December, although Liverpool can cut the gap when they host Burnley on Sunday.
It has been a difficult week for the defending champions, with Uefa and the Premier League joining Fifa and the Football Association in launching separate investigations into their financial affairs and academy recruitment.
But if those issues, along with seemingly outlandish claims from Italy that Pep Guardiola has agreed to take charge of Juventus next season, are distracting the Blues players as they chase an unprecedented quadruple, then they did not show it here.
For the third successive game, they faced a side hell-bent on stopping them scoring rather than showing any ambition themselves, but City kept at their task and eventually made the breakthrough.
Like West Ham and Bournemouth before them, Watford camped in their own half and their proximity, physicality and sheer numbers frustrated City for long spells of the first half.
Sergio Aguero should have scored when he found a rare bit of space in the box to meet Bernardo Silva’s cross, but the Argentina striker sent his header bouncing wide and Watford went in happy at half-time.
Sterling, with the assistance of referee Tierney’s interpretation of the offside rule, quickly changed that – and City did not look back.
The whole atmosphere at the Etihad Stadium was lifted, and City’s evening went from a grind to a stroll in the space of 13 minutes as Sterling added two more goals.
