Barry Hayles had put Cheltenham in front on 22 minutes, his opener owing to a slice of good luck as his close-range effort deflected off Ryan Gilligan to sneak under keeper Chris Dunn.
The lead was wiped out within 60 seconds by Akinfenwa, though, who capitalised on a ricochet and some loose marking to find the corner from 12 yards.
Hayles restored Cheltenham’s advantage with his fifth league goal of the campaign, poking home a Ben Marshall corner from close range on 30 minutes.
But the home side were again pegged back by the giant figure of Akinfenwa who a minute after the restart chased a long punt from keeper Dunn and slid a low shot under the advancing Scott Brown to claim his eighth goal of the season.
Earlier Cheltenham defender Ashley Eastham came close to a goal on his debut, heading a corner against the bar.