Tommy Rowe, John Marquis and Alfie May found the net for Rovers as they followed up their excellent win at Blackburn Rovers with another enterprising attacking display.
But they twice conceded within seconds of scoring as Blackpool refused to lie down and Darren Ferguson's men had to settle for a second successive draw on home soil this season.
Blackpool have now not lost a league game at Doncaster in nine attempts - and they maintained that record by coming from behind three times with goals from Sean Longstaff, Oliver Turton and Callum Cooke.
Rovers looked confident in possession early on and might have gone ahead following an incisive break from halfway but Marquis was forced wide and his shot was blocked by Curtis Tilt.
Danny Andrew and Liam Mandeville then went close but the home side survived a huge let-off when Mark Cullen raced clean through on goal only to pull his hamstring and play no further part in the game.
Blackpool grew in confidence and Clark Robertson headed Jimmy Ryan's freekick just wide.
Rovers had been the better side though and they went ahead on 37 minutes when Rowe crashed a half volley from distance off the bar and it went in off the back of goalkeeper Ryan Allsop.
The lead lasted barely 30 seconds as, straight from the kick off, Sean Longstaff found space 25 yards out and smashed a stunning effort past Ian Lawlor.
Rovers regained the lead in first half stoppage time when Andy Butler saw a header blocked but Matty Blair headed it back across the face and Marquis converted from close range with a clever bicycle kick.
Blackpool began the second period in determined fashion and another superb effort from distance, this time from Oliver Turton, drew them level again on 65 minutes.
Gary Bowyer's side had the bit between their teeth but they fell behind for a third time, against the run of play, when Tilt failed to clear a Matty Blair cross and substitute Alfie May was on hand to score for the third game running.
Incredibly, however, Blackpool again levelled within seconds of conceding when Longstaff played a ball into Callum Cooke who coolly slotted home from close range.
May tested Allsop from distance in stoppage time but Rovers had to settle for a share of the spoils.
Rovers: Lawlor, Mason, Wright, Butler, Andrew, Whiteman, Blair, Rowe, Coppinger (Kongolo 72), Mandeville (May 59), Marquis. Subs not used: Marosi, Alcock, Garratt, Ben Khemis, Williams.
Blackpool: Allsop, Turton, Aimson, Robertson, Tilt, Anderton (Solomon-Otobor 66), Ryan, Longstaff, Daniel, Cullen (Cooke 20), Vassell (Osayi-Samuel 89). Subs not used: Williams, Taylor, Clayton, Delfouneso.
Referee: Robert Jones (Merseyside)
Attendance: 7,558 (432)