Pep Guardiola’s men failed to win on their travels in last year’s tournament, but they strolled to victory at De Kuip against the reigning Dutch champions.
John Stones and Sergio Aguero had City two-up inside the opening 10 minutes, before Gabriel Jesus added a third midway through the first half.
The Citizens completed the rout with Stones scoring his second of the game in the second half.
City enjoyed a dream start in the second minute when Stones headed down a David Silva cross into the area and it somehow rolled through the legs of Tonny Vilhena who should have stopped the ball on the line.
On seven minutes Jesus got his head to a Bernardo Silva cross and looped his effort over keeper Brad Jones, but a defender on the line denied him a second.
However, it was 2-0 on 10 minutes when Kyle Walker got down the right and picked out Aguero in the area and he hit a sweet effort into the roof of the net at the near post.
The Argentine almost grabbed a second on 18 minutes when Bernardo Silva teed him up but Jones got down to make the save.
Feyenoord’s first effort came on 20 minutes when Steven Berghuis could only fire straight at Ederson with his weaker left-foot.
A minute later and Ederson was again called into action to tip a Michiel Kramer strike from the left of the area wide of the upright.
City responded positively and extended their lead on 25 minutes when Benjamin Mendy’s effort from outside the area was parried by Jones and Jesus was on hand to fire in the loose ball from close range.
It was almost 4-0 on 32 minutes when Kevin De Bruyne picked out the run of Aguero in the area, but he could only fire into the side-netting.
Stones grabbed his second of the game to put City four ahead on 63 minutes when he got up to meet De Bruyne’s cross following a corner and powered in a header past Jones from six yards.
Raheem Sterling almost got in on the act when he was picked out in the area by De Bruyne on 65 minutes but his angled strike was saved by Jones at his near post.