The visitors took the lead when Sam Winnall fired home from close range after Dons keeper Ross Worner parried Chris Iwelumo's shot, having dropped a near-post cross.
Charlie Sheringham wasted a golden opportunity midway through the first half after Niall Canavan handled in the box and his resulting penalty was well saved by Sam Slocombe low down to his right.
The visitors took full advantage on the half-hour when Iwelumo met Andy Welsh's far-post cross from the left with a thumping header into the roof of the net.
However, Wimbledon pulled one back on 62 minutes when Michael Smith fired home his first Dons goal since signing on loan from Charlton and Harry Pell levelled with a thumping low strike from 18 yards after Scunthorpe failed to clear their lines.
Scunthorpe thought they had won it late on but Winnall's effort was ruled out for offside before Dons substitute Arthur drilled home with three minutes to go to complete a stunning comeback.