An enthralling first half was lit up by a goal for each side inside a minute.
Stockport opened the scoring on the half-hour mark when Liam Dickinson pounced on an error by Danny Swailes before tucking a neat shot past keeper Willy Gueret.
But the hosts’ joy was short-lived as the Dons hit back with a fine strike of their own as skipper Andrews rolled the ball into Mark Wright’s path, and he curled home from the edge of the box.
Two more quickfire goals followed just before the hour mark. Sub Adam Proudlock put Stockport back in front with his first touch, but less than a minute later the Dons levelled as Alan Navarro followed up his own saved shot to make it 2-2, before Andrews looped a shot home to win it.