Roy Keane's side looked to have done enough to secure three points when they twice came from behind to lead 3-2 with 11 minutes remaining.
But Fortune curled a wonderful 25-yarder over the head of Richard Wright to earn the hosts a share of the spoils and ensure Ipswich equalled their worst start to a season in 45 years.
Waide Fairhurst had earlier given Doncaster a first-half lead, only for substitute Jack Colback to fire the visitors level in the 66th minute.
Martin Woods put Rovers ahead again with a thumping long-range strike, but two goals in three minutes from Tamas Priskin, another Ipswich substitute, and Lee Martin turned the game on its head.
Fortune then had the final say when he claimed his first goal for Doncaster with six minutes remaining.
The result keeps Ipswich in the bottom three, while Doncaster remain unbeaten at home this term.
Doncaster went into the game without influential midfielder Brian Stock, who was missing with an ankle injury. Sam Hird came into the side in Stock's absence with Rovers switching to a 3-5-2 formation as a result.
Ipswich boss Roy Keane made two changes to the XI that drew 1-1 with Nottingham Forest on Tuesday night, with Tommy Smith replacing the suspended Gareth McAuley and Pablo Counago starting in place of Jon Stead, who was named among the substitutes.
Rovers took the lead in controversial fashion in the 13th minute.
Gareth Roberts' inswinging cross was dropped by Richard Wright under pressure from Fairhurst, and the young forward reacted quickly to prod the ball into the empty net, with the visitors appealing for a foul on their goalkeeper.
Ipswich responded well to the setback, with the lively Counago seeing one effort ruled out for offside before heading inches wide.
John Oster came close to adding a second for the hosts, finding space around 25 yards from goal before firing in a dipping shot that was tipped away by Wright at full-stretch.
The visitors, meanwhile, saw another chance go begging in the 42nd minute as Smith diverted a header narrowly wide from Martin's corner.
Doncaster started the second half on the front foot but it was the visitors who had the first chance of the second half as Counago's header deflected off Hird for a corner.
And Ipswich should have been level in the 64th minute as Grant Leadbitter's delightful chipped pass found Alex Bruce unmarked in the area, only for the defender to fluff a tame shot straight at Sullivan.
The visitors did equalise two minutes later, however, as a loose ball broke to Colback on the edge of the area and the on-loan midfielder drilled home a left-footed shot which clipped the post on it's way in.
The goal visibly lifted Keane's men, but it was Rovers who went back in front when Oster's corner picked out Woods 25 yards out and the midfielder fired a left-footed strike through a crowd of players and into the bottom-right corner.
Priskin then nodded home Leadbitter's free-kick to bring Ipswich level again, before Martin made it 3-2 from close range after Smith's header had rebounded off the bar and Bruce had seen a shot cleared off the line.
However, Fortune's late strike brought the scores level once again and there was even time for further chances at both ends in a breathtaking finish.