Alfie May scored his first goal of the season - and first since December 2017 - to put Rovers ahead and end the team's three-game sequence without a goal.
But Blackpool fought back with goals from Michael Nottingham and Harry Pritchard either side of the break to book their place in the third round.
Remarkably the Tangerines' victory extended their unbeaten sequence in Doncaster to ten games in all competitions.
Rovers went ahead midway through the first half but never asserted any serious control against a big and busy Blackpool outfit.
They ended the game in rather disjointed fashion and, with several key players absent, rarely looked like finding an equaliser.
With Saturday's trip to in-form Peterborough United in mind, Grant McCann shuffled his pack and gave John Marquis, Andy Butler, James Coppinger and Herbie Kane the night off, along with suspended goalkeeper Marko Marosi.
And, if anything, the evening particularly showed the value of Marquis, whose physical presence was sorely missed up top, and Kane, whose energy and industry was absent from the midfield.
Matty Blair got his wish to play further forward and started in the front three, while Paul Taylor and Jermaine Anderson made their first Rovers starts.
Taylor was the pick of those three, playing neatly in between the lines and providing the assist for Rovers' goal. Anderson, making just his fifth senior appearance of the year, was very quiet on his debut.
The visitors made the better start and John Sullivan wasted an early opening before Nottingham headed wide from a corner.
Left back Danny Andrew was Rovers' best outlet early on and as the home side started to enjoy more possession they ought have taken the lead on 19 minutes when the lively May burst into the box and crossed for Taylor but his shot was saved by Mark Howard and he put the rebound wide.
Taylor quickly put that right by turning provider for May. He clipped a nice ball into his fellow forward's feet from the left flank and the turn and left foot finish from May was of the highest quality.
To their credit Blackpool responded well to going behind and they levelled before the break when Ben Heneghan won a back post header from a corner and Nottingham hooked in the loose ball.
Some slack defending almost let in Sullivan just after the re-start but he steered his shot narrowly wide.
Blackpool turned the game on its head on the hour mark when a throw from the right reached Pritchard who poked a shot past Ian Lawlor from close range.
Alfie Beestin, Alex Kiwomya and Issam Ben Khemis all got a taste of the action and McCann switched to a 4-2-3-1 in search of an equaliser.
But apart from a Ben Whiteman effort from distance which was comfortably saved, Howard was rarely troubled in the Blackpool goal and Rovers went out of the competition with something of a whimper.
Rovers: Lawlor, Mason, Wright, T Anderson, Andrew, Whiteman, Rowe (Ben Khemis 74), J Anderson (Kiwomya 61), Blair, Taylor (Beestin 66), May. Subs not used: Ogley, Horton, Lund, Gibbons.
Blackpool: Howard, Nottingham, O'Connor, Heneghan, Bola, Feeney (Thompson 66), Spearing, Taylor, Pritchard (Turton 74), O'Sullivan, Gnanduillet (Dodoo 85). Subs not used: Delfouneso, Cullen, Sinclair-Smith, Mafoumbi.
Referee: Anthony Backhouse
Attendance: 3,188 (192)