United thought they had earned a share of the points when top scorer Rene Howe headed in a 90th minute equaliser before the game's late twist.
The Dons scored with their first attack as striker Paul McCallum guided his header into the far corner following Rashid Yussuff's cross from the right wing on six minutes.
Wimbledon's joy was short-lived as United responded within two minutes as the visitors failed to deal with Danny Stevens' incisive run into the box.
Dons keeper Neil Sullivan saved Stevens' close-range shot but Gulls skipper Lee Mansell was on hand to fire in the loose ball.
Wimbledon regained the lead when central defender and captain Mat Mitchell-King scored with an angled drive from the left hand side of the penalty area on 33 minutes.
Forwards Ashley Yeoman and top scorer Howe both tested Sullivan with shots as United pressed for a leveller while midfielder Craig Easton should have scored after being teed up by Yeoman on 65 minutes.
Substitute Luke Moore forced United keeper Michael Poke into a full stretch save with a thumping 74th minute drive before two goals in a thrilling finale left both sets of fans breathless.