Goals from Justin Richards and Josh Low ended a drought that had lasted since September 12 as the Daggers poor form continues.
The Robins had the better of the opening exchanges as Richards had a shot turned aside by goalkeeper Tony Roberts, before Andy Gallinagh saw his header smack against the bar.
Daggers leading scorer Paul Benson had his side’s only chance of the opening period, but put his free header too close to Scott Brown.
The Robins took the lead in first half stoppage time when Julian Alsop swung over an inch-perfect cross that Richards headed home via a slight deflection.
After the break, Cheltenham extended their lead after 66 minutes when David Hutton sent Low clear and he dinked the ball over the onrushing Roberts.