Omari Hutchinson and Freddie Ladapo were on target for Town as the Blues came from 2-0 down to Premier League Wolves by the quarter-hour mark to go in at the break level at 2-2.
Town boss Kieran McKenna made 10 changes with keeper Vaclav Hladky the only survivor from Saturday’s 4-3 Championship victory over Blackburn.
Dom Ball started at right-back with Brandon Williams on the left and George Edmundson and Elkan Baggott at the centre of the defence.
Former Wolves man Lee Evans skippered at the centre of midfield alongside Jack Taylor, with the three behind striker Ladapo, Kayden Jackson, Marcus Harness and Hutchinson.
McKenna named a strong bench featuring the likes of Luke Woolfenden, Janoi Donacien, who is back from injury, Massimo Luongo, Wes Burns, Conor Chaplin and George Hirst.
Skipper Sam Morsy, who was born in Wolverhampton and started his career at Molineux, wasn’t in the 20-man squad.
Wolves also made 10 changes from the team which drew 1-1 at Luton on Saturday with forward Hwang Hee-Chan the only player to keep his place.
Centre-half Santiago Bueno made his debut following his summer move from Girona, while Tommy Doyle, who is on loan from Manchester City, was handed his first start.
The visitors took the lead via the first attack of the game in the fourth minute. Ball intercepted a deep cross from the right ahead of Hwang on the left of the box, but only diverted it out to Sasa Kalajdzic, whose first-time pass found the South Korean international, who was by now in acres of space, from where he fired across Hladky and into the net.
Wolves weren’t far from a second in the sixth minute when Matt Doherty brought the ball in from the right before hitting a shot which was goalbound until Edmundson slid in to deflect over.
Town claimed a penalty in the eighth minute after Williams burst into the area on the right but was crowded out. Referee Sam Barrott showed no interest.
Boubacar Traore was shown the game’s first yellow card on 12 for tripping Hutchinson with the on-loan Chelsea man in full flow and having already beaten Jonny Otto.
Hutchinson smashed the resultant free-kick into the wall but the ball bounced out to Evans, who struck a powerful low shot through to Wolves keeper and skipper Dan Bentley, who claimed confidently.
Wolves doubled their lead on the quarter-hour. From the second of two corners, this one on the right, Hladky superbly saved Santi Bueno’s header to his left, but Portugal U20 international centre-half Toti reacted quickest to slam the ball into the roof of the net.
Soon after the second goal, Blues skipper Evans was booked for a foul on Hugo Bueno.
Having been caught cold by the early goal and then the second before they had settled, Town had struggled to get a foothold in the game and create anything going forward.
But in the 23rd minute, after a sharp pass from Williams, Taylor forced Bentley into his first save with a shot from just inside the area to the left which the keeper pushed wide.
Wolves were still in control but five minutes later, the Blues pulled a goal back. After Hladky had cleared a ball played down the Wolves left, Harness brilliantly played in Hutchinson on the right of the box behind Santi Bueno, from where the youngster struck a shot which beat Bentley off the inside of his left post.
The goal gave the Blues confidence and in the 32nd minute Ladapo tried his luck from distance with his effort flying only just over Bentley’s bar.
Two minutes later, Evans opened up from the edge of the box and his shot similarly flew only just over.
Having started as slowly as at any time under McKenna’s management, Town were firmly back in the hunt and taking the game to the visitors with the home crowd starting to make themselves heard.
On 37, Hutchinson hit a well-struck 20-yard free-kick which was was dipping under the bar until Bentley’s fingertips intervened and turned it over for the first of two Blues corners.
And two minutes later, Town were on terms. Following throw on the right, Harness played a clever ball in to Ladapo midway inside the area to the right from where the striker hit a shot which Bentley could only help on its way into the net to send Portman Road into raptures.
In the 44th minute, Wolves were awarded an indirect free-kick inside the area after Hladky had handled a back pass from Edmundson. Before the kick could be taken, Hwang was booked for complaining that Town’s wall was in the wrong place, then when the kick was finally taken, the ball was played short to Pablo Sarabia, who couldn’t beat the massed ranks of Blues in front of him and Taylor eventually cleared.
As the half moved into injury time, Sarabia hit a low shot a couple of yards wide of Hladky’s left post.
Soon after, referee Barrott ended a topsy-turvy half in which the Blues had come from all but dead to go in level.
Town hadn’t got going by the time Wolves scored their first goal and then their second with their front players looking likely to score every time they went forward at that stage.
But after Harness created Hutchinson’s excellent goal, the Blues, who had perhaps given their top flight opponents too much respect, found their feet and began to put the Premier League side under pressure and were rewarded with Ladapo’s well-taken goal.
A tie which at one stage had looked all but over is anyone’s in the second half.
Town: Hladky, Ball, Edmundson, Baggott, Williams, Evans (c), Taylor, Jackson, Harness, Hutchinson, Ladapo. Subs: Slicker, Woolfenden, Burns, Chaplin, Aluko, Luongo, Hirst, Humphreys, Donacien.
Wolves: Bentley (c), Jonny, Doherty, S Bueno, Toti, H Bueno, Traore, Doyle, Sarabia, Hwang, Kalajdzic. Subs: King, Ait-Nouri, Kilman, Hodge, Gomes, Fernandez, Cunha, Silva, Fraser. Referee: Sam Barrott (West Riding).