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Doncaster set the pace with skipper Martin Woods starting the goal spree when he fired home in the fifth minute.
Woods started the move himself when he intercepted a pass deep in his own half before racing forward and latching onto a return ball from John Oster, which he sidefooted home first time from ten yards.
It was all Doncaster for a spell and Dean Shiels fired just wide in the ninth minute before Jason Shackell's header missed by inches following a corner.
The Blackpool goal enjoyed a charmed like when Sharp and Shields had chances blocked on the line in quick succession in the 17th minute and then Simon Gillett fired just wide.
But the home side was hit by an equaliser in the 21st minute when Ian Evatt dispatched a glancing header at the near post following a corner from David Vaughan.
Sharp missed a couple of chances to put his side back in front, but made amends within 12 seconds of the second half when he showed great reflexes to convert from close range following a left-wing cross from Gareth Roberts.
Play was swinging from end to end as Blackpool refused to give up the fight, with on-loan arsenal teenager Jay Emanuel-Thomas looking increasingly dangerous for the visitors.
And the youngster had the Blackpool fans on their feet when he dribbled threw to level the scores again with a fine finish in the 62nd minute.
Blackpool led for the first time to complete a dramatic transformation when big striker Ben Burgess scored with a splendid curling shot from just inside the box 13 minutes from time.
It looked like being enough for victory until Sharp beat the offside flag to grab a point for Doncaster with a goal in the last minute.
Substitute Paul Heffernan went close to pinching victory for the home side in injury time.