A well-taken goal from Ferran Torres and another thunderous finish from Gabriel Jesus was enough to bag all three points for the Citizens, who added a third late on through a fine João Cancelo curler.
Another clean-sheet and the return of Jesus are positives that Manchester City will take all day long. Olympiacos were heavy underdogs coming into this one, and struggled to keep City's attackers at bay in the first half.
However, the Greek side improved massively in the second half and were unlucky not to score. Here's how the Manchester City players fared in this Champions League group stage encounter.
Also check out: Champions League Draws 2020/21
Manchester City Player Ratings
Ederson - 6/10
It's now three clean-sheets on the row for the Brazilian, who didn't have much to do all evening. His passing was mostly precise, bar one occasion where he gifted the ball to the opposition cheaply.
Kyle Walker - 7/10
The Englishman has started the season in excellent form and once again put in a very decent shift at right-back. He was needed at his defensive best in the second half, with Olympiacos trying desperately to grab an equaliser, but did well under the circumstances. He also ventured forward competently when the opportunity came.
John Stones - 7/10
Considering he hadn't received much first team action this season before today, Stones did a commendable job at the heart of the Manchester City defence. His distribution was good and he won most of his aerial duels.
Nathan Ake - 7/10
Another player making his return to the Manchester City first team, Dutchman Nathan Ake had a good comeback from injury operating as the left-sided center-back. He didn't take too many risks with the ball at his feet, and completed his defensive tasks diligently.
Oleksandr Zinchenko - 5/10
The Ukrainian had a very average day at the office. Coming in for João Cancelo, who was given a well-deserved rest, Zinchenko was hardly a shadow of the influential Portuguese. He failed to provide much going forward, and also made a couple of errors at the back.
Ilkay Gundogan - 6/10
The German was excellent in the first half, crafting attacks from the middle of the park with his metronomic passing. He looked a little off the pace as the game grew older, but managed to do a fine job regardless.
Kevin de Bruyne - 7/10
The Belgian wasn't quite at his incredible self tonight, as he failed to get into great playmaking positions. Yet, he came away with two assists to his name whilst also working very hard off the ball. He should have done better with the chance he got in the second half.
Phil Foden - 5/10
An off-day for the youngster, who looked lively throughout the match in phases but failed to deliver with any sort of consistency. He made a few unforced errors which will frustrate his manager a bit.
Riyad Mahrez - 5/10
The Algerian needs a goal to start feeling good about his game again, as he continues to struggle to create or score from threatening positions. Manchester City are a much better side with Mahrez in form, and he was still a handful for opposition defenders.
Ferran Torres - 8/10
The Spaniard became the third-youngest player to score in four consecutive Champions League games when he drilled the ball through the goalkeeper's legs to open the scoring for Manchester City. His movements operating as a No. 9, despite being a winger, are excellent, and Pep Guardiola's men benefited from the same.
Raheem Sterling - 7/10
Sterling was a live wire early in the match, as he took on opponents with ease. He was a constant threat down the left hand side and came close to scoring and assisting on several occasions.
Gabriel Jesus - 7/10
The Brazilian struggled to get involved when he came on off the bench, but sealed all three points for Manchester City with a smashing finish into the roof of the net from a tight angle. His return from injury is a massive boost for City.
Bernardo Silva - 6/10
Kept things simple after coming on with 20-odd minutes left to play.
Rodri - 6/10
Added more defensive stability to the Manchester City team when they were being heavily tested by a rejuvenated Olympiacos offence.
João Cancelo - 7/10
Scored a sublime goal from 20 yards out, which was the cherry on the cake.
Felix Nmecha - 6/10
The Manchester City youngster was handed his Champions League debut and capped it with an assist. It's a night he'll never forget.