Town edged the first half but it was Doncaster who snatched the lead with an opportunist goal from 20-year-old striker Waide Fairhurst.
Fairhurst went up with keeper Richard Wright and a defender for a high ball played into the box by Jason Shackell.
But the former England keeper fumbled the ball and Fairhurst was quick to flick it into the net as it dropped towards him.It was a big blow for Ipswich, but they hit back spiritedly with Pablo Counago shaving the foot of the post with a glancing header from Damien Delaney's left-wing cross in the 19th minute.
Doncaster went close again in the 28th minute when John Oster latched onto a mistake by Tommy Smith and unleashed a fierce shot which was parried by Wright at the expense of a corner.
But the visitors went close twice again just before the interval through Jon Walters and a downward header from Smith which only missed by inches.
Ipswich battled back after the interval with on loan teenager Jack Colback firing home into the bottom corner after latching on to a loose ball that broke to him in the penalty box.
Doncaster had looked lackadaisical in the second period until then but suddenly found their form and began to attack with purpose again.
They regained the lead in the 74th minute when Oster played a corner to Martin Woods, who was standing outside the penalty box and the Rovers midfielder lashed a low left-foot shot through a crowd of players into the net.
It would have been enough to finish off most teams, but Keane's men showed their mettle when they battled back to take the lead within five minutes.
Hungarian striker Tamas Priskin headed home a free-kick from Grant Leadbitter in the 77th minute and Lee Martin forced the ball home in a goalmouth scramble a couple of minutes later after Smith had headed against the bar.
It looked as if Keane had gained his first win until Fortune popped up to score with a superb 25-yarder into the top of the net in the 84th minute leaving Ipswich without a win in eight league games.