Posh skipper Dean Holden was in the right spot to open the scoring with a firm 17th minute header and claim his first goal for the club, although teenage winger Jamie Day thoroughly deserved his captain's enthusiastic congratulations after providing a pin-point cross from the left flank.
Former Oldham campaigner Holden was close to a second but, after goalkeeper Danny Crane, one of four Diamonds captures barely 24 hours before the game, blocked his shot; James Quinn was ruled offside as he netted the rebound.
Barry Hunter, boss of struggling Rushden, who sacked his assistant and chief scout in a hectic week, was also forced to blood 16-year-old Lee Tomlin to replace suspended front man Drew Broughton.
Hunter will almost certainly have been pleased with his much-changed side's opening, as new midfielder Tony Stokes, brought in on loan from West Ham, wasted a great third minute chance when he hit the ball way over the bar.
Later after Tomlin's progress was stopped by Chris Plummer's timely tackle, Stokes was far more impressive and home goalkeeper Mark Tyler did well to reach a rising shot and palm the ball behind to prevent what looked a possible equaliser.
Posh were not as dangerous after losing wide players Ryan Semple and Day to injuries either side of the interval, but grabbed a decisive second goal with a quarter of an hour left.
Calum Willock's strong solo run came to an abrupt end when he was sent sprawling by ex-Burton Albion keeper Crane and Quinn netted with a less then convincing penalty that went in off the upright.