The Seagulls must have been counting down the minutes as City totally dominated from start to finish.
And Sterling completed his third hat-trick of the season with an unorthodox header eight minutes from time.
The victory also seals runners-up spot in the Premier League
Pep Guardiola said before the game that he enjoyed watching Graham Potter sides and the open aspect of the first half perhaps explained why.
City are used to playing sides who defend deep and in numbers, but Brighton are a side who stick to their beliefs in how the game should be played.
Of course, against an attack as potent as City’s, that brings certain risks with it.
The first real opening came on 17 minutes when Kevin De Bruyne’s corner found its way through to Eric Garcia who was taken by surprise and he connected just enough to send the ball wide from a couple of yards out.
Four minutes later, City did take the lead.
Riyad Mahrez spotted Gabriel Jesus outside the Brighton box and the Brazilian’s header found Sterling who cut inside of one challenge before arrowing a low shot into the bottom right corner of the net.
It was Sterling’s 25th of the campaign – equalling his personal best – and further cemented his position as leading scorer for the Club.
City continued to dominate and Gabriel Jesus came close to adding a second on 35 minutes when he saw a fierce shot hit the top of the crossbar, but nine minutes later, the hard-working Brazilian finally got his reward.
By the break, it felt like City had already done enough.
City carried on where they’d left off after the resumption.
De Bruyne saw another sublime free-kick thump against the post with keeper Matt Ryan rooted to the spot with 50 minutes played, but the wait for the third would only be three minutes away with Riyad Mahrez’s superb cross headed home by Sterling.
And within minutes it was 4-0, with a welcome goal for Bernardo Silva – his first in 20 Premier League games – as he followed up his own low shot by putting away the rebound thanks to Jesus’ hunger and persistence.
Fittingly, Sterling had the final say with a bizarre fifth, as he chased a pass into the box and as he fell, the ball came down, hit his head and went through the legs of Ryan for his 27th of the campaign.
Sterling work, Raheem
With 27 goals now scored this season, Raheem Sterling has underlined his reputation as one of the best forwards in European football.
The mark of any top player is consistency and quality at the highest level - and Sterling has shown that in bucket-loads.
He now has 96 for the Club from 237 appearances and with at least five games remaining this season, who would back against him reaching a century before the campaign is out?
He bagged 25 last season, but has topped that total in five games fewer this campaign.
An in-form Sterling is crucial to City’s hopes in both the FA Cup and Champions League – and he seems to be getting sharper by the game.
And could he even be making a late surge for the Golden Boot?
He is five behind Jamie Vardy and on this display, anything is possible.
Pep Guardiola: 'Credit to Sterling'
“All the credit is for him. Not just for the three goals, but they are important for what we have ahead of us.
“For his development as a player, because he wants to improve. We are delighted with his performance today.”
Unused subs: Carson, Otamendi, Doyle, Palmer
What it means…
City are guaranteed the Premier League runners-up spot after moving 12 points clear of Chelsea with three games remaining.
With 91 goals scored so far, it’s also likely that City will comfortably finish the division’s top scorers.
City host Bournemouth on Wednesday (18.00pm kick-off) in the Premier League and will then take on Arsenal at Wembley in the FA Cup semi-final next Saturday (19:45 KO).