Substitute Akinfenwa rose to plant home a firm 88th minute header from the outstanding Danny Jackman's corner to stretch the Cobblers' unbeaten run to four games.
Swindon, with £200,000 signing Simon Cox a spectator in the stands due to a wrangle with Reading which delayed his registration, struggled to break down a well-organised Northampton defence.
In a scrappy first half Swindon keeper Petr Brezovan kept his side on level terms with an outstanding point-blank save from Ryan Gilligan, while the Robins' woeful finishing saw first-half substitute Blair Sturrock and defender Jerel Ifil waste the half-chances that came their way.
It was not until the 53rd minute that Northampton keeper Mark Bunn was first called into action when he turned Anthony McNamee's cross over the bar.
However, three minutes later he was picking the ball out of his net after Sturrock caught the Cobblers defence napping, nipping in front of his marker to tuck home Miguel Comminges' long throw.
Swindon at last began to ask questions of the Northampton defence and Mark Little's superb last-ditch tackle denied Swindon the cushion of a second goal as Lee Peacock attacked Christian Roberts' cross.
But Northampton, prompted by the outstanding Jackman, responded and their neat football got its reward with Akinfenwa's late equaliser.
The goal was harsh on Swindon skipper Hasney Aljofree who again was in commanding form at the centre of his defence.
The Cobblers, who had won their three previous games, might have rubbed salt into the wounds and ended Swindon's eight-game unbeaten run had Jonathan Hayes converted a half-chance in stoppage time when he sliced wide from a tight angle.