The scoreline hardly reflected City's almost total dominance on the night with the 22-2 shot ratio in our favour telling it's own story.
Now City will look to finish as group winners with two games still to play.
City were on the front foot from kick-off with a high press forcing the Greek side to almost exclusively camp in their own defensive third.
The passing was fast, clever and slick and there was greater urgency around the box in what became a rather tetchy opening period.
But, as so often when City roll into town, the opposition put every man behind the ball meaning space in and around the box was at a premium.
It was total dominance with Ederson redundant at the other end and the only surprise was it took 35 minutes to break the deadlock – and it was worth the wait.
The excellent Ilkay Gundogan played a long ball forward to Gabriel Jesus who played Sterling in on the left of the box and his sublime back-heel gave Foden the chance to bury a low shot past the keeper from close range.
It was City at their best and it was fitting reward for Foden who had been delving into his box of tricks all evening.
The hosts’ discipline faltered as the half wore on and City came close to doubling the lead on 45 minutes when Sterling’s powerful free-kick was well saved by Jose Sa as the ball headed for the top left corner.
It was same again after the break with City dominant and Olympiakos clinging on.
Bernardo, Cancelo and Sterling could have all added to the lead and the fact that City had 22 shots to Olympiakos' two off-target efforts, suggest the confidence in front of goal is still not where it needs to be.
In fact, that would probably be Pep Guardiola's only concern of an otherwise superb performance by a team who are making the chances as much as in the goal-laden previous three seasons.
CLASSY ilkay PIVOTAL TO CITY'S UCL BID
Ilkay Gundogan may not hog the headlines on a regular basis but his understated excellence - particularly in the Champions League - is crucial to our hopes of winning this competition.
Creative. intelligent and combative - Gundogan was all these things and more against Olympiakos as he made his 36th appearance for City in the UCL.
On the rare occasions the Greek side attempted to break free of their defensive shackles, invariably it was Gundogan who was on hand to break-up play and win the ball back.
No wonder he is a regular in Pep's Champions League starting XI.
Phil Foden's performance had a bit of everything, capped with an excellent deciding goal.
What it means…
City have qualified for the Round of 16 with maximum points from the first four group matches.
City entertain Burnley at the Etihad this Saturday with a traditional 3pm kick-off.
Then we are back in action in the Champions League with a trip to Porto the following Tuesday (8pm)
Stats and facts
The seven shots on target in the first-half of this game was the most by any team in the Champions League so far this season.
City have never lost a game that Phil Foden has scored in (W16 D1).
City have qualified for the last 16 for the past eight seasons in succession.
It is the first time since the 1969/70 campaign that City have kept three clean sheets in a row in European competition.
News about Olympiakos v Man City
Olympiakos 0-1 City: Short highlights
City made it four group stage wins from four with a 1-0 win over Olympiakos Watch more.