Durrell Berry opened the scoring midway through the first half with a well-taken finish, before AFC Wimbledon’s Jack Smith levelled shortly before half-time.
The Dons had the better of the second half, but Cheltenham goalkeeper Trevor Carson stood firm.
AFC Wimbledon started well and should have opened the scoring in the 20th minute through midfielder Alfie Potter, but he fired straight at Carson after a fine turn and run inside the box.
But against the run of play the visitors took the lead five minutes later through Berry. The full-back ran into the box and drove a low right-footed shot off the inside of a post.
The Dons were level one minute before the break. Potter crossed from the left and Akinfenwa teed up Smith, who headed home from close range.
The hosts had a great chance to win the game two minutes from time, but Carson produced a brilliant save, tipping substitute George Oakley’s close-range shot on to a post.