George Elokobi's 75th-minute red card for a tough challenge on James Coppinger left the Barclays Premier League visitors clinging on for their second chance.
Hunt's penalty had cancelled out Rovers' half-time lead with Billy Sharp and James Hayter scoring twice in as many minutes to cancel out Nenad Milijas's stunning long-range opener.
But with the action swinging from end to end and both sides having clear-cut chances, it provided rich entertainment for Rovers' lowest crowd of the season, 8,616.
If the Doncaster public did not give the game much importance, the same could not be said of Wolves manager Mick McCarthy, who made only four changes to the side that humbled Chelsea last time out.
And his faith almost paid off instantly when Stephen Ward flashed a left-foot shot wide of target within the opening 30 seconds, setting the tone for an action-packed tie.
At the other end, a poor third-minute clearance by Richard Stearman fell to Joseph Mills and his cross from the left found Sharp, who mis-kicked in the box.
As the end-to-end action continued, Stearman took a run towards the Rovers goal and tried a rising left-foot shot which was knocked out for a corner by Rovers keeper Neil Sullivan.
Then it was Rovers' turn to come close again when Hird rounded off a spell of penalty-box pressure by dipping a left-foot shot which dropped just wide of Marcus Hahnemann's left-hand post.
Sharp had the ball in the net in the 12th minute when he turned home a cross from the lively Mills but referee Anthony Taylor ruled it out for a foul by Sharp on Christophe Berra.
A diving James Hayter was close to connecting with a cross from the right by James Coppinger in the 19th as Sean O'Driscoll's side threatened to take control.
The excellent Mills drilled a low shot at Hahnemann but it was Wolves who grabbed the lead in the 38th minute when Milijas hit a stunning 35-yard effort past Sullivan from the left flank.
Any thoughts that the visitors could rest easy until the break were extinguished three minutes later when Sharp was fed by a short pass from Coppinger and drilled home the equaliser.
And the Championship side went ahead in the 43rd minute when John Oster's header into the box fell to Hayter, whose swinging right-foot volley beat Hahnemann again.
The pace slackened a little after the break as Wolves took control, David Jones hitting a long-range effort over the bar before McCarthy's men notched their inevitable equaliser.
Sam Hird could have few complaints following the trip on Matt Jarvis which led to referee Anthony Taylor pointing to the spot, and Hunt duly stepped up to squeeze home the spot-kick to Sullivan's left.
Ward twice came close to putting Wolves in front and Jarvis also fired just high but the visitors' most dominant spell was brought to a shuddering end in the 75th minute.
Elokobi clattered into Coppinger on the halfway line and after lengthy treatment and plenty of frayed tempers on the touchline, the Wolves man was handed a straight red by Taylor.
Doncaster manager O'Driscoll hailed Hayter for the 43rd-minute strike which briefly put Rovers in front but admitted being disappointed by the prospect of a replay.
"For James to get as much power on his shot was excellent," said O'Driscoll.
"James is always going to get chances. I've watched those centre-backs curtail Fernando Torres and Didier Drogba in recent weeks and his goal was first class.
"But a replay is just a matter of more games for us. The more games we play the more chance we have of picking up injuries, and we have an extremely small squad."
O'Driscoll said he had no complaints over the award of a penalty after Sam Hird tripped Matt Jarvis in the box, but also admitted he thought the sending-off of Elokobi was harsh.
"At the time I thought the referee had given the penalty a little bit quickly but I've since seen it on DVD and I have to admit it was a definite penalty.
"I think if the sending-off was for violent conduct it's very harsh. If he sent him off for a reckless challenge I'm not sure whether it was just a yellow. It's a difficult one."
McCarthy claimed the dismissal of Elokobi cost his side victory.
"I think it's harsh," said mcCarthy.
"George has not led with his elbows or his knees – he's gone to head the ball and his momentum has taken him into him.
"I think the decision was influenced by some of their players and the crowd's reaction. One (player] was giving out to George while he was on the floor and I don't like that.
"We deserved our equaliser in the second half and with 11 men in the team we were in the ascendency and likely to win.
"It might not have proved that way, but there looked like one winner."
McCarthy said the rest of the game was played in a "great spirit", adding: "We could have done without a replay but even more so we could have done without a defeat.
"It must have been a good game to watch and it was a proper FA Cup tie. We took the lead with a fabulous goal and they equalised with a fabulous strike.
"I'm sure both of us will say we might have won."
Doncaster Rovers: Sullivan, Chambers (Friend 64), Lockwood, O'Connor, Mills, Coppinger, Wilson, Hird, Oster, Hayter (Brooker 90), Sharp. Unused substitutes: Gary Woods, Martin Woods, Webster, Fairhurst.
Wolverhampton: Hahnemann, Doherty, Stearman, Berra, Elokobi, Jarvis, Edwards (David Jones 28), Milijas, Hunt, Ward, Fletcher (Doyle 69). Unused substitutes: Hennessey, Mujangi Bia, Davis, Winnall, Batth. Sent Off: Elokobi (77).
Referee: A Taylor (Cheshire).
Man of the match: James Hayter.
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