Two minutes after entering the fray on the hour, Woodrow struck his third goal for the Reds with a deft finish to cancel out an opener from Herbie Kane ten minutes earlier.
The strike from Woodrow preserved Barnsley's unbeaten run at Oakwell, which extended to 16 games - with the Reds last seeing their colours lowered on home soil on March 17.
But that had keeper Adam Davies to thank at the death, with the keeper making a fantastic save to deny James Coppinger - who hit the crossbar early on - with the last action of the game.
Forced into a defensive rejig with Tom Anderson suspended, Rovers switched right-back Niall Mason to the centre and his sterling performance characterised an impressive opening half from the visitors.
They went closest to breaking the deadlock on eight minutes when Coppinger cut inside and unleashed a fine shot which struck the woodwork in a half in which Rovers showed intent, quick-thinking and quality on the ball with their work ethic being relentless.
After a slow opening, Barnsley - who promoted Mike Bahre and Ryan Hedges to the starting line-up - started to gradually show one or two promising signs, but it was a half in which the honours went to Rovers, who gave the hosts something to think about without managing to make the breakthrough.
Prior to Coppinger's chance, only a saving tackle from the commanding Ethan Pinnock denied the lively Ali Crawford, while devotees to the art of defending will have similarly enjoyed a fine saving tackle from Mason later on in the half to stop Kieffer Moore in his tracks.
Moore had one or two half-chances, seeing a steered header fly wide and firing a shot straight at Ian Lawlor, but the danger chiefly came from Doncaster.
Alfie May fired an early chance for Rovers, with the half ending with Bahre's deflected shot flying off target.
On the resumption, Rovers crowned a very presentable performance with an opener to stun the hosts, seven minutes in.
Cavare failed to clear his lines and the ball found Coppinger, whose deadly centre was bulleted home by the head of Kane.
It was no more than Rovers deserved, with the Reds given even more to think about.
In a bid to pep up his side, Daniel Stendel threw Woodrow and George Moncur and it reaped almost instant reward.
Doncaster switched off from a direct ball forward and Potts flicked the ball on and Woodrow seized onto the ball in an instant before delicately steering the ball past the advancing Lawlor.
It was a relieving moment for the Reds, who soon started to sense blood as Rovers started to look rocky for the first time.
Moore steered a header over before livewire Woodrow saw his shot fly straight into the arms of Lawlor.
After weathering a mini-storm, Doncaster rallied late on and should have taken the lead 15 minutes from time when Marquis sent May clear after a mistake from Bahre, but the nine-goal striker - fresh from his four goal haul in midweek - blasted over with the goal at his mercy, with his wait for his first league strike of the campaign continuing.
Soon after, Kane was just off target with a long-ranger before super defending on two occasions from Cavare stopped certain goals for May and Coppinger before a brilliant late save from Davies denied Coppinger a dramatic winner - after the Rovers veteran was set up by Kane following an error from Cavare.
Barnsley: Davies, Cavare, Pinnock, Lindsay, Pinillos (Woodrow 60), Mowatt, McGeehan (Moncur 60), Potts (Thiam 80), Bahre, Hedges; Moore. Substitutes unused: Greatorex, B Williams, Adeboyejo, Brown.
Doncaster Rovers: Lawlor, Blair, Mason, Butler, Andrew, Crawford (Rowe 69), Whiteman, Kane, May (Wilks 82), Marquis, Coppinger. Substitutes unused: Marosi, Beestin, Taylor, Blaney, Cummings.
Referee: M Salisbury (Lancashire).
Attendance: 13,573 (1,863 Doncaster Rovers fans).