City struggled to break down their determined hosts in the opening hour as home striker Alfie May had the Town dreaming of an incredible upset.
However, it wasn’t to be in the final ten minutes as a Phil Foden inspired City finally edged their way through.
City dominated possession as expected in the opening half hour but Cheltenham skipper Ben Tozer denied them a opener as he headed Benjamin Mendy’s drive off the line.
The visitors did look to up the tempo a notch or two after the break as Gabriel Jesus wasted a brilliant chance.
And that lack of decisiveness was to cost City on the hour mark as May reacted quickest to Tozer’s long throw as he smashed home past Zak Steffen.
That goal tested City nerves in the final 10 as man of the match Foden finally volleyed them level.
That intervention cracked the Cheltenham confidence in the final few minutes however as a ruthless City powered with strikes from Jesus and Ferran Torres.
Full Time at the brilliantly named Jonny Rocks Stadium it’s Cheltenham 1 Manchester City 3