Substitute Ian Morris scored the only goal of a poor game 11 minutes after the interval, with victory for the in-form Cobblers giving them real hope of avoiding an exit out of the Football League despite still occupying a place in the drop zone.
Exeter shaded a nervous first half where there was little quality on show. They had the best chance with Sam Parkin laying the ball across goal and on a plate for David Wheeler but he spurned a golden opportunity by firing into the side-netting.
Tom Nichols and Matt Oakley both had shots blocked for Exeter while Liam Sercombe dragged a shot wide from 25 yards, Northampton's one chance of the half came when Emile Sinclair smashed a good chance high over the crossbar from 15 yards.
Town improved after the break and went in front when they broke down the right and Chris Hackett crossed for Morris, who volleyed into the ground and the ball looped over Artur Krysiak and into the net.
Exeter showed little fight after that and Northampton always looked the more likely to score but neither goalkeeper was really tested in a dismal game of football.