Doncaster captain Brian Stock scored a goal in either half to secure his side a fourth-round tie against Aston Villa.
The home side deservedly went in front when Martin Woods' free-kick cannoned off the bar into the path of Stock, who tapped in from six yards.
Doncaster doubled their lead when Woods' corner fell to John Spicer whose shot ricocheted for Sam Hird to finish from close range.
Stock secured the win, lashing home a superb half-volley from 25 yards.
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Goals: Stock 26, Hird 36, Stock 58.
Cheltenham: Brown, Lindegaard, Duff, Gallinagh, Ridley, Bird (Durrant 77), Wright (Hayes 46), Russell, Owusu, Hammond, Vincent (Watkins 69). Subs Not Used: Puddy, Fathers, Maynard.
Booked: Vincent.
Att: 5,345
Ref: Stuart Attwell (Warwickshire).
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