Doncaster settled into a pattern of quick, sharp passing in the first half and could have gone ahead from one of a couple of good chances in the early stages.
Paul Heffernan nodded over from close range after Martin Woods had found him with a left-wing cross and Town goalkeeper Scott Brown had to be at his best to deny Heffernan shortly afterwards.
Brown fell upon a shot from Sam Hird midway through the first half, but the Robins stuck to their task well and kept Doncaster at bay with Andy Gallinagh holding the back four together.
The home side almost stole the advantage shortly before half-time when midfielder David Bird met a right-wing cross from Andy Lindegaard with a downward header, but Rovers goalkeeper Neil Sullivan got down to it in the nick of time.
The second half followed a similar pattern with Doncaster seeing plenty of the ball without finding a way through a well-organised Cheltenham rearguard.
Brown stretched to touch a long-range drive from John Spicer over the crossbar then dived to save from Hird at the start of the second half.
The best chance of the game fell just past the hour mark when Heffernan turned sharply in the box and although his shot beat Brown, just about the only thing that did all night, the ball bounced back off the post.
Cheltenham could even have snatched it right at the end when Bird's shot was blocked on the line and spun out just wide of Lloyd Owusu, who was waiting for the tap-in.