The visitors could adjudge themselves unfortunate, seeing their winless streak stretch to five games after failing to make the most of their possession.
The game started at a sluggish pace, with the first chance coming on 15 minutes when Cody McDonald saw his drive blocked by Stevenage keeper Chris Day.
The visitors had little cutting edge and they had to wait until the half-hour mark before conjuring their first real sight of goal, Byron Harrison seeing his header pushed wide by Alan Julian.
Stevenage appeared the better side, but all that changed on 38 minutes, the hosts taking the lead when Akinfenwa glanced Danny Spiller's cross past Day.
The visitors continued to press after the break, but McDonald wasted a host of chances to seal the win as the Gills played effectively on the break though Stevenage came close to a point late on when Julian produced smart stops from Rob Sinclair and Ben May respectively.