A superb David Templeton strike and a Lucas Akins penalty saw Burton twice lead in a game which they had much the better of the attacking play.
But Jon Taylor and Kieran Sadlier both responded in quickfire fashion to earn a point for Doncaster.
After a strong start, Burton finally broke the deadlock after 36 minutes when Templeton curled in a wonderful effort from the corner of the box.
Doncaster were level just three minutes later. After James Coppinger saw a shot saved by Kieran O'Hara, who then blocked a follow-up on the line, Taylor rifled home.
Burton regained the lead from the penalty spot in the 53rd minute. Donervon Daniels was caught in possession and dragged down Joe Sbarra as he tried to recover, with Akins slamming home the penalty.
But again, the visitors' lead was short lived when Doncaster equalised in fortunate circumstances four minutes later as Sadlier raced through and saw his initial shot saved by O'Hara, only for the ball to ricochet in off the goalkeeper.