Two goals inside the final six minutes saw Town leave Wimbledon empty handed having overturned a 1-0 deficit to lead late in the game.
Paul Kalambayi headed the hosts into a half time lead, but goals from Matty Daly and Alex Pattison early in the second half had turned the tie on it's head.
That was until the 84th minute when Courtney Senior grabbed an equaliser, with Josh Davison grabbing the winning goal four minutes later.
Simon Weaver made one change from Tuesday's trip to Walsall as Jack Muldoon returned from injury to take the place of Miles Welch-Hayes.
Wimbledon started the stronger of the two sides and had the ball in the net after six minutes when Harry Pell finished off Josh Davison's low cross, only to be flagged offside by the linesman.
Pete Jameson's first involvement came in the 16th minute as the Town stopper stuck a leg out to keep out Assal's low effort across goal.
Town had settled into the game and put together a series of passing moves, with Matty Daly playing an influential role, but couldn't find a way to test the Dons 'keeper.
The only goal of the first half went the way of the hosts six minutes before the break as Paul Kalambayi headed home from a corner to give his side the lead.
Town pulled level two minutes after the restart as Daly claimed his third goal in three games, following up Luke Armstrong's saved shot after Muldoon and Pattison had worked the ball to the striker.
The turnaround was complete 20 minutes later as Jaheim Headley's corner was turned back into a dangerous area by Muldoon towards McArdle to turn goalwards, with Pattison grabbing the final touch on the line.
Muldoon went close to making it three from another dangerous Town corner, but the hosts cleared and were able to pull themselves back on level terms in the 84th minute.
Jameson has only partially cleared a long free kick into the Town box, with Senior nipping in before Coley could clear to loft into the empty goal.
Pattison went close to restoring Town's lead soon after when getting onto Armstrong's flick and trying to chip the keeper, but was a fraction off target.
With two minutes of normal time remaining Davison claimed the Wimbledon winner, cutting inside and finding the bottom corner to complete the second turnaround of the afternoon.
Pattison would again go close in stoppage time, but the crossbar prevented a dramatic late equaliser, with Wimbledon's stopper also denying Armstrong after Tyler Frost's dangerous delivery.
Town: Jameson, Falkingham, Burrell, Grant (Coley 80), Headley, Pattison, Muldoon, Ramsay (Frost 94), McArdle, Daly, Armstrong
Subs not used:Oxley, Welch-Hayes, Folarin, Ferguson, Horbury
Goals: Daly 47, Pattison 65
Wimbledon: Tzanev, Gunter, Woodyard (Bendle 83), Kalambayi, Pell, Davison, Assal, Chislett (Hudlin 69), Towler, Maghoma (Senior 69), Currie
Subs not used: Broome, Frimpong, Ogundere, Marsh
Goals: Kalambayi 39, Senior 84, Davison 88
Booked: Currie, Hudlin
Referee: Paul Howard
Attendance: 7,620 (237 away)