Injury-hit Vale's poor first half started as it meant to go on with their only chance coming after eight minutes when Leon Constantine's 20-yard shot deflected wide to avoid testing Alan Blayney.
Dave Mulligan's shot two minutes later summed up the early frustration when he ballooned his long-range effort wildly over Mark Goodlad's crossbar.
Michael McIndoe's corner provided Steven Foster with the perfect opportunity to give his side the lead in the 24th minute but the captain squandered the free header, putting it wide.
However, Doncaster did open the scoring in the 27th minute when Paul Heffernan made no mistake in heading Mulligan's right-sided cross firmly into Goodlad's top left corner from 12 yards.
Donny should have doubled their lead before the half was out when Sean Thornton's neat flick into Foster looked like producing a certain goal but he sidefooted over from only six yards.
Vale got the goal they had been crying out for ten minutes after the break when Constantine's flick-on caught the defence napping with Sam Togwell taking advantage, smashing home a left-footed shot from close range.
A transformed hone team took the lead in the 73rd minute when Steve Rowland's cross from the right was pulled back to the edge of the area where Togwell waited to fire a half-volley into Blayney's top corner.
Doncaster's attempts to freshen up their tired players with three substitutions seemed to do little good as Vale clung on to their slim lead to make the fourth round for the first time in ten years.