Potters boss Tony Pulis made 10 changes to the team that defeated Aston Villa on Saturday but his team still contained enough pace, strength and sharp passing ability to stay one step ahead of the hard-working Robins.
The first half was extremely tight with Cheltenham content to soak up the best that Stoke could throw at them while trying to initiate breakaways when they could.
The home side's cause was aided by some wayward finishing by the Premier Leaguers, who could have gone ahead through defender Ryan Shawcross on eight minutes but his effort was straight at Cheltenham goalkeeper Shane Higgs.
Vincent Pericard headed wide from a Richard Cresswell cross and shortly before half time, Pericard set up Cresswell for a shot that he dragged well wide.
A goal finally arrived six minutes after the re-start when Cheltenham defender Shane Duff conceded a free-kick on the edge of the area and Stoke midfielder Glenn Whelan curled an expert shot around the wall and into the top left-hand corner of the net.
Cresswell doubled the lead four minutes later when he raced onto a long kick from goalkeeper Steve Simonsen that Pericard flicked into his path.
At that point the game was heading only one way but Cheltenham made it interesting when Ashley Vincent ran onto a loose ball in midfield. His pace took him away from the Stoke defence and he scored with a low shot off the right-hand post.
Cheltenham pressed for an equaliser but they were caught on the break 12 minutes from time when Danny Pugh got away on the left and crossed for Jon Parkin to score with a crisp half-volley from the edge of the box.
Alex Russell drove in a consolation goal deep into injury time but Cheltenham, without the services of the three loan players who have made them look a better side in recent weeks, were seen off comfortably enough.