Brad Kilner gave United a flying start with a second-minute minute goal but they were unable to build on it and Shaun Mundy equalised for the Doncaster side on the stroke of half time.
With neither side able to break the deadlock in the second half the game went into extra-time during which Kilner scored the winning goal in the 105thÂ minute.
The clash between the sides top and bottom in North One went the way of the form book with title favourites Clay Cross Town posting their ninth win of the campaign when dishing out a 7-1 beating to Thorne Colliery, whose consolation goal was scored by Kirk Frost.
Leaders Crowle Colts made it seven wins from eight in Division One North following their 4-2 victory at Welbeck Lions Reserves. Tom Finnigan, Josh Simpson, Ricky Girling and Danny Smyth all found the net.
Second-placed Sutton Rovers maintained their title challenge when beating Epworth Town Colts 5-3 after twice being two goals down toÂ Â claim their sixth win in eight starts.
The home side led 2-0 at the break and regained their two-goal lead when hitting the target for a third time after Callum Stockton had pulled a goal back for last season's Doncaster Rovers Senior League champions four minutes into the second half.
Rovers drew level just after the hour mark with goals by Adi Parker and Luke Chambers, who added a second, as did Stockton, in the last ten minutes.