After the early dismissal of Hornets striker Mathias Ranegie, Chris Brown headed Rovers in front after 24 minutes.
But Watford were left seething as Rovers goalkeeper Sam Johnstone failed to see red or concede a penalty despite hauling down Troy Deeney just before the break.
The visitors shrugged off that setback to equalise though Ikechi Anya, and just as it looked like they had done enough to earn a point, up popped Sharp to send the home fans home ecstatic.
After an uninspiring opening, the first shot after 16 minutes required Johnstone to dive low to his left to keep out an effort from Alexander Merkel.
But the game turned on its head two minutes later as Watford were reduced to 10 men with Ranegie being shown a straight red by referee Chris Sarginson for kicking out at James Husband.
Husband tackled the big Swede down Rovers' left flank and after Husband appeared to pat the big frontman on the head, Rangie responded with a swift kick in the full-back's direction, leaving Sarginson no choice.
The one-man advantage paid dividends just five minutes later as James Coppinger, whose wife gave birth to a baby girl on Saturday, swung over a cross which was headed home by Brown at the near post.
David Cotterill then sent an effort just wide of Jonathan Bond's left-hand upright as Rovers started to crank up the pressure.
Five minutes before the break Watford should have been back in it, but to the amazement of virtually everyone inside the Keepmoat Stadium, Johnstone failed to concede even a free-kick as he rugby tackled Deeney in his own box as the Hornets striker latched on to a sloppy Abdoulaye Meite backpass.
Deeney nicked the ball past Johnstone and as he was about to roll the ball into an empty net, the keeper instinctively hauled him down, but referee Sarginson gave nothing, a decision which enraged the visitors' dugout.
Rovers received another lifeline after 51 minutes, Merkel striking a 20-yard free-kick against the bar, with Deeney quickest to react, but he could only divert his first-time effort two yards over with the goal at his mercy.
Hornets boss Beppe Sannino sent on Fernando Forestieri to give his side some attacking thrust just before the hour mark as, despite the silky skills of Cristian Battocchio and Daniel Tozser in the centre of the park, they were struggling to create clear-cut chances.
And Watford finally drew level on the counter-attack after 67 minutes, with Forestieri scooping a lovely pass to Anya who took a couple of steps before slamming the ball into the bottom left-hand corner.
Rovers almost took advantage of a dozing Watford defence moments later as Sharp latched on to Coppinger's cross, but his effort looped on to the top of the net.
It was Watford's turn to breathe a sigh of relief after 78 minutes as Mark Duffy jinxed his way into the box to cross for Brown, whose scuffed effort from inside the four yards somehow bobbled inches wide of the far post.
Richie Wellens was denied by Bond, Cotterill's shot was hacked off the line by Deeney, before Brown headed over, all within the space of 30 seconds, as Rovers hammered at the door.
Bond then flew to his left to keep out Duffy's free-kick as Rovers, urged on by 6,000 home fans, sensed the win was theirs for the taking against the tiring 10 men, who were defending stoutly.
And as the game entered its dying embers, Sharp pounced to stab home the winner in injury time after Bond could only parry a shot from Brown.