The Brazil striker came off the bench to turn a tight contest at the Etihad Stadium City’s way with a ferocious finish nine minutes from time and Joao Cancelo added a late third.
Manchester City had taken a 10th-minute lead through Ferran Torres but were coming under increasing pressure and conceding chances when Jesus, making his comeback from injury, intervened.
The result maintained Manchester City’s three-point lead at the top of Group C and kept them well on course for a place in the last 16.
It looked like being a comfortable night early on, with Pep Guardiola’s decision to rest centre-backs Ruben Dias and Aymeric Laporte ahead of this weekend’s clash with Liverpool seeming a smart one.
They were quickly into their stride and it looked like being a busy night for Olympiacos defender Pape Abou Cisse, who cut out a Phil Foden cross and blocked a Riyad Mahrez shot in the opening minutes.
Kevin De Bruyne then forced a save from Jose Sa after a mistake from Ruben Semedo and it came as no surprise when Torres opened the scoring on 12 minutes.
The Spanish winger may have been unexpectedly thrust into a centre forward’s role due to injuries but he has adapted to it superbly.
Once again he looked a natural as he played a one-two with De Bruyne and then calmly side-footed past Sa for his third goal in as many Champions League games this season.
Ferran Torres (left) has been thrust into a centre forward’s role (Martin Rickett/PA)
Olympiacos tightened up in defence after conceding but Manchester Manchester City continued to probe. Raheem Sterling put the ball in the net again at the second attempt after a save by Sa but then saw the flag raised for offside.
Gundogan had a shot deflected over and Kyle Walker had a dangerous cross cut out by Sa as City ended the first half in control.
Remarkably, from that position of dominance, Manchester City slackened off after the break.
Mady Camara fluffed a chance when presented with a free header at a corner and Manchester City then had a real scare when Foden woefully underhit a passed across his own area. Mathieu Valbuena swooped and should have equalised but, fortunately for Foden, blasted wide.
Youssef El-Arabi then showed excellent control to create a shooting opportunity but Stones took the power out of his effort and Ederson saved.
Making it three!
— Manchester City (@ManCity) November 3, 2020
Guardiola tried to enliven his side by summoning Jesus from the bench.
Yet Olympiacos were growing in confidence and former Watford defender Jose Holebas flashed a shot across goal after racing past Walker.
De Bruyne attempted to get into the game more and had a shot saved by Sa before a Jesus strike was blocked.
The substitution then paid off as Jesus raced onto a pass from De Bruyne and lashed a shot into the roof of the net from a tight angle to put the result beyond doubt nine minutes from time.
Olympiacos’ hopes were ended and Cancelo wrapped up the scoring with a long-range strike in the last minute.