AEK have historically struggled on English shores, winning only once in six trips, and they were on the back foot from the get-go here.
In the end, City needed just 12 minutes to reap the rewards of their early dominance: Enzo Fernandez’s free-kick cannoned off the crossbar, and Elliott Anderson tapped it in for his first goal for the club.
Enzo Maresca's men were relentless throughout the first half, and they went tantalisingly close to doubling their advantage when Allan also struck the crossbar, only this time with no one to fire in the rebound.
The Cityzens’ superiority deserved more than a single strike, and their endeavours paid off 10 minutes before half-time.
After an exchange of passes with Rico Lewis near the byline, Phil Foden poked a shot high into the roof of the net to give his side a bigger cushion.
The 2022/23 winners of the competition ought to have taken a three-goal lead into half-time, but some Alberto Brignoli heroics in the AEK goal prevented Rayan Cherki from scoring at the near post.
For all the positives City have shown this season - at least on the pitch - they have occasionally looked frail defensively, and AEK took full advantage after the break to get back into the game.
There was an element of simplicity to how they halved the deficit, as a lung-busting, untracked run from deep saw Stavros Pilios latch onto Zini’s measured ball in behind before slamming home at the near post.
City, though, possess huge quality up front, and it didn’t take them too long to reestablish their two-goal cushion when Cherki stroked a left-footed effort into the corner from the edge of the area.
Shortly after, City put the game to bed with another impressive goal.
Cherki was involved again, floating a perfect ball in behind the AEK defence, which Lewis teed up for Foden to sweep into the top corner on the half-volley.
The home team weren’t done there, either, as Foden completed his first-ever Champions League hat-trick 15 minutes from time when he tapped home Ryan McAidoo’s cross from six yards.
Maresca’s men seemingly heeded AEK’s plea for mercy at that point, content to have ended their rotten four-match winless home run in Tuesday European fixtures.
The Greek side, meanwhile, are now winless in 20 Champions League away games, and they face the tough task of trying to beat Real Madrid next.
Flashscore Man of the Match: Phil Foden (Manchester City)