Sterling's hat-trick means he has 17 league goals this season, and a total of 27 in all competitions - making this his most prolific club campaign
City had lost their three previous away league games, including a defeat at Southampton last Sunday, but they never looked like suffering another slip-up on their return to the south coast.
Sterling, who now has 27 goals in all competitions for City this season, inflicted most of the damage on a Brighton side who never managed to make the game a contest.
The England forward put Pep Guardiola's side ahead with a superb low finish from outside the area, collecting a Gabriel Jesus flick and cutting in from the left before firing into the opposite corner of the net.
More chances followed for City, and Jesus had a shot deflected against the bar before he got on the end of Rodri's knockdown from a corner to make it 2-0.
The punishment did not end there for the Seagulls, as City continued to pour forward with Kevin de Bruyne pulling the strings, although a 19th league assist of the season eluded him
The Belgian fired a free-kick against the post after half-time and it was his driving forward run that led to Riyad Mahrez crossing for Sterling to head home City's third goal at the far post.
Moments later it was 4-0, when Mat Ryan spilled Bernardo Silva's shot and the Portuguese followed up to tap home.
Sterling, whose previous hat-tricks came against West Ham and Italian side Atalanta, had the final word in bizarre fashion when he chased a pass into the area and saw the ball bounce off the back of his head and cross the line as he was challenged by Ryan.
Brighton were completely outclassed and did not manage a single shot on target.
City knew before the weekend that they were sure of finishing in the top four, but they will not know if they will be in next season's Champions League until Monday, when they find out the result of their appeal against their two-year ban from Europe.
They are still in this year's competition, however, and their chances of negotiating a tricky looking route to next month's final are surely improved by Sterling's fine form in front of goal.
He already had four goals in six games since the Premier League restarted and his haul at Amex Stadium means he has now surpassed the 25 club goals he scored last season and has made this his most prolific personal campaign.
Jesus, too, was able to add to his tally despite some poor finishing early in the game, and he has now hit the 20-goal mark in all competitions.
Even without the injured Sergio Aguero, there is clearly no shortage of firepower in this City side, although far tougher assignments than this one lie ahead.
"I was pleased with everything tonight - the result and the levels we reached," Guardiola told Sky Sports afterwards. "We are now at a good level and are ready to play the last games of the Premier League and in the Champions League.
"We've forgotten the Southampton result as we played incredibly well there. Football sometimes is strange. We just didn't score there. We're a team who create a lot of chances and this time we converted them."
Brighton endure a difficult night
Brighton still need five more points from their remaining three games to be mathematically certain of safety, although their eight-point cushion over the bottom three currently appears healthy enough.
It was just as well their survival was not reliant on them getting anything here, as City tore into them and met little resistance.
The Seagulls went toe-to-toe with Liverpool in midweek and competed admirably with the new champions after conceding twice in the first 10 minutes, but this was a very different evening against the team the Reds have just deposed.
There were no early mistakes that cost Graham Potter's side this time, but they had to battle all game to keep out a relentless City side and enjoyed few opportunities at the other end.
"City were too good tonight," Potter said. "We were well beaten by the better team.
"First half, we were in it a bit and had a couple of opportunities but they have got players that can hurt you everywhere.
"We are disappointed with how we petered out in the second half but it's a big ask to play Liverpool and City in the space of four days."
Man of the match - Raheem Sterling (Manchester City)
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