It was fitting that this clash should be decided by one of Posh's three central defenders, as they snuffed out the home threat which was diminished with the decision to start with leading goalscorer Scott McGleish on the substitutes bench.
The only goal arrived in the ninth minute when Ryan Semple delivered a cross from the left after the home defence failed to adequately clear a corner and Plummer struck with a first-time volley into the corner.
It was the first goal Northampton had conceded in five matches and, despite Peterborough's indifferent recent form - it was their first win in five matches - they dug in grittily to keep home chances to an absolute minimum.
Home shots were restricted in the first half to wayward long-range efforts by Eoin Jess and Josh Low, while Andy Kirk also missed the target from 30 yards.
In fact Plummer could even have had a second for the visitors in the 25th minute when he headed a Semple corner wide and in first-half stoppage time Paul Carden volleyed over the crossbar.
It could only get better for Northampton and they did create two respectable second-half chances, although Kirk was unable to bury either of them.
In the 57th minute the ball ran loose to him from a tackle on the edge of the box but he could do no better than fire straight at Mark Tyler who saved with his legs.
Then, seven minutes, later a long throw from Northampton's best performer David Hunt was nodded on by Ian Taylor only for Kirk to send his close-range header wide of the target.
As Northampton's scrambles became increasingly desperate, Posh might have nicked a second in the closing minutes when Trevor Benjamin seized on a short back header from Chris Doig but the striker was crowded out.