After their FA Cup heroics against Middlesbrough this was a lacklustre performance by jaded City, who went off to a loud cry of "what a load of rubbish".
Victory, though, came at some cost for Cheltenham, as their new signing Scott Brown set an unwanted record, being stretchered off for the second time in five weeks.
The first time he was a City player and then a leg injury in a 2-2 draw at Cheltenham turned out not to be as serious as first thought.
Now, having switched clubs, his first start lasted only ten minutes before he collided with new team-mate Damian Spencer on the edge of the box.
There was a long hold-up before he could be rushed to hospital with a suspected broken leg.
The visitors, always the better side on the night, won it with a shot from Spencer just before the break.
City, who have made three window' signings, had two of them on from the start and Wayne Andrews made a promising start as he spun off Shane Duff to win a corner.
Nothing came of it, or Cheltenham's first corner, badly overhit by J.J. Melliga,n but John Ward's side soon proved a threat.
Melligan robbed Bradley Orr 40 yards out and headed towards goal.
Defenders were able to regroup to hustle him out of the shot, but the message was clear and after Brown's injury Melligan underlined it with a right-foot volley which had the keeper taking off to cover his left post.
Melligan, rather surprisingly, was taken off in the second half as manager John Ward looked for the extra pace Kayode Odejayi could provide.
City were under so much pressure they were finding it difficult to get any shape into their game and a sequence of free-kicks against them didn't help. More than half an hour went by before Andrews got in their first shot, which drew a dive from Shane Higgs.
But it was Cheltenham's night and on 44 minutes they got the goal they deserved when Jamie McAllister gave away one of several free-kicks, just inside the left touchline.
Melligan drove it in, Spencer's header was blocked, but came back to him and he tucked the second chance into the bottom right corner.