Harding almost caught Oxford napping with a deft chip while Clarke Carlisle headed over as Cobblers made the better start.
Oxford were slow to get into their stride but former Cobbler Liam Davies tested Lee Nicholls with a low drive and Damian Batt fired wide.
Cobblers still created the better chances, though, Adebayo Akinfenwa heading over and ex-Oxford winger Chris Hackett forcing Luke McCormick to save at his near post. In between, Tom Craddock was denied by Nicholls as Oxford got into the contest.
But Cobblers finally broke the deadlock on the stroke of half-time when McCormick could only palm out Hackett's testing cross and Harding fired home from 15 yards.
James Constable was denied by Nicholls after the restart, Andy Whing mis-kicked from close range before then seeing his header punched clear by the Cobblers 'keeper.
Akinfenwa missed a great chance to double Northampton's advantage as Oxford pressed for a late equaliser, substitute Deane Smalley heading just over while Constable was twice foiled by Nicholls.