Grigg kept his cool after an error from Kyle Walker in the 79th minute to slot beyond Claudio Bravo and book a quarter-final place for Paul Cook's League One side, ending Pep Guardiola's quest for a historic quadruple in the process.
Aymeric Laporte and Fernandinho wasted glorious chances for City in the first half, but their task was complicated by Fabian Delph being sent off for a rash lunge on Max Power.
Wigan still had to withstand long spells of pressure after the break, doing so magnificently, before Grigg coolly dispatched his seventh goal in as many FA Cup matches this season.
"It's brilliant – obviously it was a nice easy game out there," Grigg joked when he spoke to BBC Sport after the match.
"It was an unbelievable performance by the lads. They're probably the best team in Europe at the moment
"I caught the offside trap and it was a nice little foot race with Kyle Walker, which was not really what I wanted.
"I'm a goalscorer. I've said I'll score at any level and luckily that one's gone in."
Asked whether he had thought a victory that mimicked the scoreline of Wigan's famous win over City in the 2013 FA Cup final was possible beforehand, Grigg replied: "To be honest, probably not. We worked really hard. The gaffer and the staff have put a great game plan together.
"Even before the sending off we were playing really well. It comes at a good time but it's one of those things.
"Against a side like that – you can see in the second half that they've dominated possession.
"They've got some unbelievable players, some of the best players in the world and we defended unbelievably well."