Town went down to a Stephen Ward goal despite creating a host of chances, with Owen Garvan hitting the bar with a header.
Ward capitalised on a rare mistake by David Wright on 32 minutes and rounded Lewis Price to score from a narrow angle.
Town dominated possession for long periods and peppered the Wolves goal with Garvan sending a header against the woodwork, Alan Lee twice denied by Matt Murray in the visitors' goal and Jon Walters seeing a late header go agonisingly wide.
Jason De Vos returned to the Town line-up after recovering from a cracked metatarsal, with Chris Casement making way after playing against Watford on Saturday.
Lee was back in the team after suspension with Walters partnering him in attack after being Cup-tied for the defeat at Vicarage Road, Danny Haynes starting on the bench.
Lee was immediately in the action, heading on for Gary Roberts whose cross was cleared by Rob Edwards at the near post.
Walters then sent Lee clear with the Republic of Ireland international testing Murray with a fierce volley that the 'keeper held at the second attempt.
Murray had a much easier save to make minutes later from a Matt Richards long range effort while at the other end, Wolves had their first effort on goal on 15 minutes, Michael McIndoe's drive taking a deflection off Alex Bruce and forcing Price into a smart save.
Murray held Lee's looping header from Jaime Peters' cross, Dan Harding then flashing the ball across goal as Town looked the more likely to score.
Peters tested Murray again from 25 yards, the 'keeper holding the ball under pressure from Lee, Blues then having a penalty appeal turned away after Roberts' cross hit Karl Henry.
Despite creating little in the first 30 minutes it was the visitors who took the lead, the normally dependable Wright's backpass intercepted by Ward who rounded Price and scored from a tight angle.
Town responded, Lee's header forcing Murray to concede a corner, then Roberts sending a volley dipping just over the bar.
The former Accrington player then had a free-kick deflected over as Town continued to dominate the play, Sylvain Legwinski going close with a flick at the near post.
McIndoe picked up an early booking for kicking the ball away at the start of the second-half, Wright then doing well to block Andy Keogh's cross from the byeline.
Walters ghosted past Neill Collins on the edge of the box but his shot was charged down, Murray beating Lee to the loose ball, Keogh then stretching to clear Roberts' dangerous cross as Town searched for the equaliser.
Just before the hour Price produced a brilliant save to deny Michael Kightly on a Wolves breakaway, the Welsh international flying to his right to palm the ball away.
Seconds later Town should have been level, Peters and Walters combining to set up Richards who volleyed over from 15 yards.
The game swung from end to end, De Vos doing superbly to block Ward's goalbound shot after Wolves had men over in the box.
In an open game chances were arriving at either end, Roberts hooking over from Lee's header then Bruce deflecting Keogh's cross into his own net but the offside flag was raised.
Lee then diverted the ball over the bar from close range before the striker was replaced by Haynes on 67 minutes, Garvan also coming on for Roberts.
Both substitutes were immediately in the action, Garvan testing Murray from 25 yards with a low strike, then Haynes sending a fierce drive across goal.
Legwinski's surging run at the Wolves defence then created an opening for Walters, whose shot was parried by Murray, the visitors then clearing from Walters as he tried to turn in the box from Peters' cross.
Price saved from Keogh but Town continued to crave out openings and Garvan rattled the crossbar with a header, Richards' follow up shot blocked by a sea of Wolves' legs at the nearpost.
Wolves were inches away from a goal on the break on 80 minutes, Keogh's cross was heading for Ward but Wright got across to prevent an open goal.
Keogh was then replaced by Jody Craddock as the Molineux side looked to defend their lead for the last 10 minutes, Town bringing on Billy Clarke for Legwinski with Jay Bothroyd on for Kightly.
Walters headed just inches wide again from Peters' cross as Town threw everything at the Wolves' goal, Harding denied by Edwards' challenge but Blues couldn't find the equaliser the play certainly deserved.
Town: Price, Wright, De Vos, Bruce, Harding, Peters, Richards, Legwinski (Clarke 82), Roberts (Garvan 67), Lee (Haynes 67), Walters. Subs not used: Supple, Casement.



















