Next-to-bottom Rushden showed the kind of never-say-die spirit that just might keep them in the Football League this season whereas Cheltenham will just be glad to have collected three more points.
The home side turned on the style at times during the first half and although Rushden had their chances, Cheltenham were clinical with their finishing.
They took the lead after only seven minutes when a flowing move of several passes ended with a left-wing cross from Brian Wilson and JJ Melligan scored with a diving header in off the crossbar.
The lead was doubled six minutes later when Grant McCann was fouled 25 yards from goal and Wilson stepped up to stroke an inch-perfect shot around the defensive wall and inside goalkeeper Scott Tynan's left-hand post.
Veteran midfielder Darren Caskey was the most potent threat for the visitors and he forced two good saves from home goalkeeper Shane Higgs as well as setting up striker Drewe Broughton for a shot he placed just over the bar.
But the Robins gave themselves a three goal cushion on 33 minutes when Rushden cleared their lines following a corner and Wilson played the ball back into the area. One defender had taken his time in getting up field so John Finnigan was left onside. The Cheltenham captain took a touch before tucking a left-foot shot in off the inside of the near post.
Rushden boss Barry Hunter made a double substitution at half-time and the changes paid off eight minutes after the re-start when young striker Simeon Jackson produced a nice turn of skill to get between two defenders and send a low drive beyond Higgs.
Still Cheltenham looked capable of adding to their total and Tynan was forced to save well from Steve Guinan, while Melligan blazed wide from a good position and substitute David Bird struck a long-range shot against the post.
Finnigan cleared one off the line from John Turner but the final quarter of the game was a hard slog as Cheltenham shut up shop and Rushden toiled to find a way through.