It was Rushden who started the better and after three minutes Mark Tyler failed to hold Marcus Kelly's free-kick and the ball fell to Greg Pearson, who should have done much better with his effort.
A minute later another good chance fell to Rushden but Chris O'Grady fired well over with his effort.
Peterborough defender Mark Arber then saw his back header intercepted by Jason Taylor, but he sent his shot inches wide.
Despite the hosts dominating the early stages it was Peterborough who opened the scoring in the 21st minute when Arber headed down Paul Carden's cross and the ball fell to Richard Logan to apply the finish.
Chris O'Grady again had an excellent chance in the 32nd minute when he rose to head Kelly's corner inches over.
Shortly after the restart Kelly made a fine run down the left for the home side but he saw his cross fire wide by Neil McCafferty.
Rushden suffered a setback when skipper Peter Hawkins was sent off for a foul on Adam Newton, his second bookable offence.
Newton then burst down the right, but Trevor Benjamin was unable to get onto the winger's cross.
After 68 minutes Jamie Young did well to smother a shot from Logan, before, at the other end, Ashley Nicholls fired over from 25 yards out.
Peterborough put the game beyond doubt after 77 minutes when Peter Kennedy found Peter Gain on the left and he cut in and easily shot past Young.
Rushden suffered further humiliation when eight minutes from time when Drewe Broughton, who had come on as a second-half substitute, collected a second yellow card for a late tackle on Sean St. Ledger.