The Premier League leaders continued with their 100% start to the season as Raheem Sterling’s 88th-minute goal gave them victory over their visitors.
They have now won all five matches to stay on 15 points, six points clear of second-placed Shakhtar Donetsk, who were beaten 3-0 by Napoli also on Tuesday.
With City already confirmed to play in the knockout stages and Feyenoord already fallen out, Napoli and Shakhtar will battle for the second group spot in the final matchday.
Elsewhere, Tottenham Hotspur also secured top spot of Group H after coming from behind to defeat Bundesliga side, Borussia Dortmund 2-1 in Germany.
Dortmund needed a win to keep alive their slim hopes of progressing to the last 16 and they took the lead in the first half when Pierre-Emerick Aubameyang swept in his 16th goal of the season.
But England striker, Harry Kane equalised for the visitors barely four minutes into the second half before Son Heung-min’s curled finish wrapped up the win late on.
In the other game of the group, Spanish champions, Real Madrid destroyed Apoel Nicosia 6-0 to seal second place and a spot in the knockout stages.
In Spain, Liverpool were delayed from qualifying for the round of 16 just yet after Sevilla came from three goals down to level, thereby snatching a point from the encounter.
The English side remain top of Group E but must avoid defeat when they host Spartak Moscow on 6 December to ensure they advance to the knockout stages.
Spartak were held 1-1 at home by Maribor.
In Group G, Turkish champions Besiktas also wrapped up top spot and qualified for the last 16 for the first time in 31 years after securing a 1-1 draw with Porto in Istanbul.
The visiting Portuguese side silenced the vociferous home crowd with the opening goal through defender Felipe, but Besiktas midfielder Talisca equalised before half-time to secure their place in the knockout stage.
Meanwhile, French champions, Monaco were thrashed 4-1 at home by Bundesliga side, RB Leipzig who remain contenders for the second spot of the group with Porto – both having seven points each.