Sharp's late goal denied Barry Ferguson a first win in caretaker charge of Blackpool.
Andy Halliday looked to have given the home side a win with his debut strike on 78 minutes, but Sharp popped up with a late header to salvage a draw for Rovers.
It was one-way traffic in the first half as a rejuvenated Blackpool looked to stem a run of nine defeats from their last 10 games.
The Seasiders were full of endeavour from the whistle and Steven Davies might have put them in front had he not been hauled down by Bongani Khumalo as he sped through on goal, 18 yards out.
The defender was fortunate to be shown just a yellow card, and although Billy Sharp headed wide from a James Coppinger cross two minutes later, the hosts continued to probe a rattled visiting defence.
On nine minutes, a ball over the top of the back four from Isaiah Osbourne set Michael Chopra free in behind, but the striker could only fire straight at the advancing Ross Turnbull.
With the next attack the hosts carved out another good opening. This time Davies was the architect when he sent a delivery across the face of the goal from the left, only for Chopra to inexplicably miss the ball completely six yards out.
The tangerine tide continued to consume the Doncaster half and, with the opening period drawing to a close, Chopra was denied by Turnbull for a second time, with his turn and shot palmed around the post from close range.
The visitors were largely redundant in an attacking sense, but on the stroke of half-time another Coppinger delivery from the right found Sharp and his header flew narrowly wide of the right-hand post.
There was still time for one final moment of goalmouth action and unsurprisingly it again went the way of the home side. Chris Basham rose highest to meet Nathan Eccleston's corner-kick at the near post and the midfielder headed wide when he ought to have found the back of the net.
The start of the second half read a similar script to the first, with Blackpool enjoying the better of the possession but lacking a sprinkling of quality in the final third as they looked to break the deadlock.
Slowly, Doncaster began to turn the tide and Coppinger forced Matt Gilks into making two decent saves - the first a low shot from the edge of the box on 63 minutes and the second a curling 20-yard effort the Pool keeper clawed away from the top right-hand corner.
Tiredness appeared to be creeping into the legs of the men in tangerine and Paul Dickov's side should have taken the lead when a lofted Paul Keegan pass found Chris Brown inside the area, only for the striker to blaze over the bar.
But just as the visitors looked to have taken control, a hopeful ball into the box by Jack Robinson ended up at the feet of Davies, and although he could not connect with his shot, substitute Halliday prodded home from close range to give Blackpool the lead.
Ferguson's side looked to have snatched victory but, with the clock ticking down, Sharp got the faintest of touches on a David Cotterill free-kick to give Doncaster a share of the spoils.