Rovers, who had been on a terrible run in recent games, were worthy winners and always looked the more dangerous side throughout the match.
Following Saturday's disappointing defeat to Southend, Northampton looked flat and failed to seriously trouble keeper Steve Phillips throughout the 90 minutes.
Rovers made a bright start and Steve Elliott should have scored after only two minutes when Northampton failed to clear a corner and he shot wide with the goal at his mercy.
Elliott then headed over from Stuart Campbell's corner as Rovers looked to take advantage of Northampton's shaky start.
The Cobblers gradually got into the game with Ryan Gillingan going close with a 25-yard drive that was just wide of the mark and then firing over moments before the interval.
In between Sean Rigg wasted a good opportunity for Rovers when he broke into the box only to shoot weakly at Mark Bunn, while Poul Hubertz called Phillips into action at the other end for his one and only save of the match.
Rigg went close in first-half stoppage time when his low drive hit the post and bounced off Bunn for a corner and, shortly after the re-start, Campbell forced the Northampton keeper into a smart save with his low drive.
Gilligan was just off target again for Northampton on the hour after a neat build-up, but a minute later top-scorer Andy Kirk shot into the side-netting after being set up by Bradley Johnson.
But Northampton still struggled to create any clear openings and it was Rovers who looked the more likely winners.
Lambert missed a great opportunity on 66 minutes when he fired over from a good position, but made amends in the 70th minute when he found himself in space to powerfully head home from Campbell's corner.