Chris Doig conceded a penalty early on that was converted to give Kleve the lead. Constantine thouh scored from the spot when Northamton won a penalty just before half time.
With 15 mins to go Town took the lead through Jason Crowe. Ian Henderson did well to set up Crowe for a tap in.
Cobblers then scored a third with Alex Dyer having a tap in after a parry by the keeper.