Alfie May’s first goal in 2018 ended a personal barren run of 13 games to open the scoring.
But the Tangerines progressed to the third round for the first time in nine years thanks to goals by Michael Nottingham and Harry Pritchard.
John O’Sullivan and Nottingham were both guilty of missing the target with easy chances for the visitors and, at the other end, Paul Taylor fired straight at Blackpool goalkeeper Mark Howard from seven yards and shot wide from the rebound.
Rovers, who made four changes from the side that started Saturday’s 0-0 home draw with Portsmouth, forged ahead on 23 minutes when Taylor played a ball into the box from the left that May gathered before turning and rifling home.
It was all square before the break. Ben Heneghan won a far-post header from a right-wing corner and Nottingham flicked the ball in from seven yards.
Blackpool took the lead on the hour mark when Nottingham’s long throw from the right skimmed off the head of home defender Tom Anderson and went in off an unwitting Pritchard.
Doncaster Rovers: Lawlor; Mason, Wright, T Anderson, Andrew; Whitman, J Anderson (Kiwomya, 61), Rowe (Ben Khemis, 74); Blair, May, Taylor (Beestin, 66). Unused substitutes: Ogley, Lund, Horton, Gibbons.
Blackpool: Howard; Nottingham, Heneghan, O’Connor, Bola; Spearing, Taylor; Feeney (Thompson, 66), O’Sullivan, Pritchard (Turton, 74); Gnaduillet (Dodoo, 85). Unused substitutes:Mafoumbi, Sinclair-Smith, Delfouneso, Cullen.
Referee: Anthony Backhouse (Cumbria).