Veteran winger Peter Beagrie hit a stunning last-minute free-kick to seal a 1-0 win in a game United dominated, but struggled to make a breakthrough.
Scunthorpe boss Brian Laws admitted: "We are going to have games like this, but it is important to maintain the pressure.
"I am delighted with the three points, how we achieve them is another matter, but it was a piece of quality and magic that won us the game.
"Rushden came with a job to do and the first-half was a no contest. Our goalkeeper Paul Musselwhite had nothing to do in the game.
"We huffed and puffed in the first half and our passing was a cause for concern but we regrouped at half time.
"We have had a tough month, but a win is a win - with patience and ability the key to success."
Law's opposite number Barry Hunter was shattered by the end result.
He said: "We put up a magnificent performance, they did everything I asked of them against a side going for promotion.
"I am not singling anybody out as outstanding although Mark Williams did well in his first game.
"We created a couple of chances, but we did not gamble as we might have done in the box.
"The players are devastated at the result and we felt we deserved a point."