Out-of-sorts City were sunk by an early Cheltenham goal after an error-strewn performance at Valley Parade.
Having defended so stoutly at Swindon the week before, City fell behind to a soft goal after just eight minutes.
James Spencer picked up a long ball before squaring for Kaid Mohamed, whose shot from inside the box squirmed under Matt Duke.
Michael Bryan drove straight at Cheltenham keeper Jack Butland but the visitors had control of the early play.
Marlon Pack, who scored from long range when the sides last met, was shooting on sight again. Duke redeemed himself with a fine diving save to his left.
Bryan thought he should have had a penalty after his cross appeared to strike Russell Penn's right hand.
But Cheltenham nearly had a second when Spencer just failed to convert Darryl Duffy's cross after a City free-kick routine had comically broken down at the other end.
City got more into the game towards half-time and Marcel Seip glanced a header across goal from a corner.
Duke saved from Duffy at the start of the second half but looked very uncomfortable from Cheltenham corners and Michael Flynn came to his rescue, heading off the line from Mohamed.
City's ragged performance continued as Seip and Flynn got in each other's way, the Dutchman recovering in the nick of time to tackle Penn on the edge of the box.
Kyel Reid volleyed well over before another misunderstanding between Seip and Duke nearly let in Duffy. The catalogue of mistakes continued.
Sub Ross Hannah at least forced a save but there was never a hint of a comeback on such a flat afternoon.
Cheltenham's sixth win in seven games had never looked in doubt.
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