Last season's play-off semi-finalists won for only the third time this season while Dagenham slipped to their first defeat in eight games in all competitions.
After a dismal opening half-hour the game suddenly burst into life thanks to Jamie Cureton's 250th career goal
The 38-year-old looped in a super effort from 25 yards to register his third of the season for the Robins.
The lead only lasted nine minutes, however.
Dagenham skipper Abu Ogogo levelled matters as he side-footed home after Rhys Murphy's initial effort had been beaten away by Cheltenham goalkeeper Scott Brown.
The visitors retook the lead just before the hour mark when Troy Brown dragged a cross back from the byline and fellow centre-back Keith Lowe was perfectly placed to head home from close range.
Murphy, Ogogo and Zavon Hines all went close late on for Dagenham but the hosts just could not find an equaliser.