The Tangerines, who had lost nine of their last 10 matches coming into this game, showed few signs of their previous poor form as they looked to forge an early lead.
The returning Michael Chopra, who hadn't featured in the dying embers of Paul Ince's reign as manager, almost found a way through. However, the former Cardiff City forward was unable to lift the ball beyond the Doncaster keeper.
Blackpool continued to enjoy good attacking play and Chris Basham's fizzing effort from distance, midway through the opening period, flew agonisingly over Turnbull's crossbar.
Halliday fired home past Turnbull and it seemed that Blackpool would hold on for a win, but Paul Dickov's men produced a late fightback and Sharp's goal six minutes from time rescued a point.
The Southampton loanee nearly snatched all three points seconds later when his effort came back off the bar, but the draw was enough to help Rovers out of the relegation zone.
The result means that Blackpool stay in the bottom half of the Championship.