A game which could have gone either way was finally decided on the last play when the Cumbrians turned defence into attack.
Winnger Shane Toal collected a loose ball from a kick meant for his opposite number - a last throw of the dice by scrum-half Matty Beharrell after the hooter had gone - to race 85 metre try to complete a 32-22 win.
The Dons had looked likely winners when they added to their 12-8 interval lead - a scoreline which flattered the visitors - after opening up an eight-point gap with a try in the corner by winger Josh Rickett from a cut-out pass close to the line.
But two close-range converted tries at the end of a third quarter the Dons had dominated gave the Cumbrians a 20-16 lead.
Although they had started to lose their way by then, the Dons bombed a great chance to regain the lead on 72 minutes when new signing Danny Bravo broke down the left only for Rickett to put down his pass, which was slightly behind him, with a clear run to the line.
What could have been a score of 20-all with the kick to come suddenly became 26-16 to Barrow as stand-off Jamie Dallimore rounded off a good move down the left and also added the extras.
Needing to score twice to win, something which always looked beyond them, the Dons were thrown a late lifeline by centre Jason Tali which set-up a grandstand finish.
The Dons had led 12-2 at one stage in the first half with prop Ryan Boyle capping an impressive opening spell with a close-range try.
Winger Sam Doherty, who was adamant after the game that he had got the ball down, had a try disallowed after cutting inside before prop Brandon Douglas scored another close-range try.
Little had been seen of Barrow in attack in a second quarter dominated by a Doncaster side which had grown in confidence and often looked dangerous when they moved the ball out wide, until they scored a converted try just before the break.
Dons: Logan, Rickett, Smeaton, Tali, Doherty, Boas, Beharrell; Spiers, Carter, Boyle, Foster, Ollett, Horne. Subs: Peltier, Douglas, Cross, Bravo.