The goal was created by Steven Gillespie and transfer-listed winger Martin Devaney, who combined cleverly down the left-hand side giving the latter the chance to cross.
His low centre was met by Brian Wilson and he drilled a shot beyond goalkeeper Alan Blayney from close range.
Midfielder Craig Dove sent Diamonds first chance of the game well over the bar and Gillespie also missed the target at the other end, but it was not long before Cheltenham doubled their advantage.
Wilson turned provider this time, supplying Gillespie with a pass in between two defenders. Gillespie shot low from 20 yards and the ball squirmed under Blayney's body to give him a first Football League goal.
At that point Cheltenham were well in control but they gifted the visitors a lifeline on the half-hour mark.
Grant McCann received the ball on the edge of his own area and instead of playing safe, he attempted to lift the ball back over his head not realising that there was an attacker on his shoulder.
That attacker was Andy Burgess and his pass gave young striker Jason Taylor the chance to beat Shane Higgs with a low drive.
Despite this setback, Cheltenham settled into their passing game right from the start of the second half and restored their two-goal advantage with 58 minutes played.
Cheltenham midfielder Dave Bird won the ball after some hesitant play by the Diamonds midfield and threaded a pass through for Devaney who beat Blayney with a low shot.
The game was over 21 minutes from time when another good pass from Wilson set Gillespie free in the area.
Rushden defender Rob Gier brought him down and referee Trevor Parkes pointed to the spot.
McCann made no mistake with the spot kick to complete Cheltenham's biggest victory of the season.