Rovers went ahead in the fourth minute when Michael McIndoe latched on to a back-pass blunder by Sagi Burton and fired home from a narrow angle.
But the rest of the half belonged to Peterborough, who hit back to equalise in the 27th minute and they looked favourite to go on and win the game after Rovers had midfield ace John Doolan sent off.
Doncaster always looked in trouble against the pace and power of the Posh's big striker Clive Platt, and Peterborough had another weapon with Andy Legg's long throw, which proved difficult to deal with.
Legg hit the crossbar with a 20-yard free-kick which took a deflection in the eighth minute, and when the ball rebounded, Burton followed up to fire inches wide.
McIndoe missed a great chance to make it 2-0 when he headed wide from Jermaine McSporran's left-wing cross two minutes later.
But it was otherwise one-way traffic as Peterborough gained a grip in midfield to lay siege to the Doncaster goal.
Platt equalised in the 27th minute with a tremendous header when he rose above three defenders to power Adam Newton's right-wing cross into the back of the net.
Doolan was dismissed in the 40th minute for an off-the-ball offence involving Burton and Rovers were fortunate not to be behind at the interval with keeper Andy Warrington coming to the rescue to save from Calum Willock and Danny Sonner in quick succession.
But it was a different story in the second half as the home side showed tremendous grit and determination despite being a man short.
Gregg Blundell and Nick Fenton went close with Warrington doing well to save again from Richard Logan at the other end.
Rover's persistence paid off when Green raced onto a great through ball from Neil Roberts to hit a stunning 25-yard effort into the bottom corner three minutes from time.