Ferran Torres scored early on before Jesus climbed off the bench to seal victory towards the end of the game.
Joao Cancelo added a superb late third as City made itt three wins from three to preserve a 100% start to Group C.
City’s aim was to get ahead and get the job done as efficiently and quickly as possible with Liverpool looming on the horizon next Sunday.
Accordingly, City began very brightly, moving the ball around with pace putting Olympiakos under the cosh from the word go.
Looking for the early strike. Kevin De Bruyne, latching on to an error in the Greek side’s defence, went close before the deadlock was broken less than a minute later.
It was a slick move that saw Ferran Torres play a one two with De Bruyne and then take it past Pape Abou Cisse with an exquisite first touch before slotting an angled shout through the legs of the on-rushing José Sa with just 12 minutes on the clock.
It was no more than City deserved and was just the start Pep Guardiola wanted.
Raheem Sterling had the ball in the net just past the half-hour but the assistant referee’s flag was raised and the effort was chalked off.
Sterling was leading Jose Holebas a merry dance on the left flank as the Greek side struggled to stem the sky blue tide, but they dug in and held on to the break to give themselves half a chance of getting back into the game after the break.
And Olympiakos, much better after the restart, almost made City pay for not making more of the first half dominance when Phil Foden almost gifted Mathieu Valbuena an equaliser with a sloppy pass across his own box but the French midfielder shot wide from six yards out.
It was frustrating for Guardiola who almost certainly would have hoped to have rested one or two of his key men ahead of Sunday earlier, but with the game on something of a knife-edge, it wasn’t possible.
And Jesus took a little more than 10 minutes to remind City fans what they’d been missing with a superb, angled shot into the roof of the net on 81 to seal victory.
It was just the return the Brazilian needed and with a huge game to come on Sunday, a gentle nudge to the boss that he is ready to resume striking duties if needed against the Merseysiders.
And it was another super sub who put the icing on the cake with a 25-yard curling effort almost on full-time to end the contest,
Torres the talisman
Three Champions League games and three goals, Ferran Torres could be City’s talisman in the competition this season.
The 20-year-old was on target against Porto and then again in the match away to Marseille.
That he added a third goal in the group stages with a classy finish against Olympiakos bodes well for City this season.
With injuries to Sergio Aguero and Gabriel Jesus denying City an out-and-out striker for much of the campaign so far, Torres looks set to be an added bonus for Pep Guardiola with his finishing proving he is an excellent finisher.
Add his superb movement and positioning and the young Spaniard is proving to be an excellent addition to the team.
20y 248d - Ferran Torres is the third-youngest player in Champions League history to score in four consecutive appearances, behind Kylian Mbappé (18y 120d) and Erling Haaland (19y 107d). Astute. #UCL— OptaJoe (@OptaJoe) November 3, 2020
What it means…
City top Group C with maximum points from three games.
Porto are second with six points and Olympiacos are third with three.
Marseille have no points from three matches.
A draw away to Olympiakos in Matchday 4 will guarantee progression to the Round of 16 for City.
It’s back to Premier League action City take on Liverpool at the Etihad on Sunday (kick-off 4.30pm), prior to a two-week international break.
Stats and facts
City have scored 44 goals in our last 16 UEFA Champions League matches; over the last two seasons our record is W16 D3 L3 with 60 goals scored and 22 conceded.
City are unbeaten in 10 home European matches (W9 D1) since a 2-1 loss against Lyon on Matchday 1 in 2018/19.
3 - Since conceding five goals against Leicester, Manchester City have conceded only three goals in their following eight games, while they have kept a clean sheet in three consecutive matches in all competitions for the first time since September of last year. Priorities. #UCL pic.twitter.com/ZROjH2AWxp— OptaJoe (@OptaJoe) November 3, 2020