The Dons took the lead through Alan Bennett's first-half header, his first goal since joining on a free transfer at the beginning of the month, but they remain rooted to the foot of the table.
Despite the delayed kick-off due to a power cut the hosts started brightly and broke the deadlock after 28 minutes.
Chris Hussey's in-swinging corner found Bennett at the back post and the centre-back headed home unmarked.
The goal sparked the visitors into life and almost immediately Roy O'Donovan fired a shot into the side-netting and Lewis Hornby saw a dipping volley fly just wide.
Akinfenwa had two efforts just after the break but Wimbledon were still a threat with Toby Ajala shooting straight at Lee Nicholls from close range.
But Northampton drew level after 75 minutes when O'Donovan collided with keeper Neil Sullivan and Akinfenwa slotted home his 17th goal of the season from the spot.