Dougie and Murphy strike but Town have to settle for a pointTown stretched the unbeaten run to five games but had to settle for a point after twice edging in front.
Jonathan Douglas scored for the second successive game to give Blues the advantage but James Henry had Wolves back on level terms before the break.
Daryl Murphy followed up his hat-trick at Rotherham with a close range finish but the visitors grabbed a point through Benik Afobe’s header.
Mick McCarthy stayed with the same side that beat Rotherham so convincingly before the international break, while Wolves included former Town loanee Jordan Graham in their line-up.
Cole Skuse fired over with the game’s first opening but the visitors went straight up the other end and had a real chance when Afobe got on the end of a ball over the top but couldn’t make it count.
It needed a brilliant tackle from Christophe Berra to deny Dominic Iorfa giving Kenny Jackett’s side the lead as Wolves caused problems on the break again, Skuse then doing equally well to put Graham’s cross away from danger six yards out.
It was Town who got the breakthrough though on 16 minutes, Jonas Knudsen supported the counter-attack down the left and from his cross, Douglas found the net with the outside of his right foot.
Carl Ikeme had an anxious look back after watching his clearance cannon back off Brett Pitman and drift over the bar.
Marton Fulop’s name echoed around Portman Road on 21 minutes as a mark of respect from the Blue Army for the former Town ‘keeper, who passed away recently - the Hungarian international wearing 21 while at the Club.
Pitman headed inches wide from Freddie Sears’ cross as Blues threatened a second, then the summer signing from Bournemouth saw his cross from deep hit the bar.
Sears burst deep into Wolves territory and then picked up a return pass to cross from the right, the ball begging to be tapped in but to no avail.
It was the visitors who found an equaliser though on 38 minutes, Graham’s corner was knocked back across goal by Mike Williamson and Henry toe-poked the ball across the line.
Ikeme was in the right place to hold firm from Tommy Smith’s header as a bright opening half came to an end with honours even.
Dave Edwards couldn’t get any power on his header as the second-half got underway, Murphy seeing his shot deflected over at the other end.
Murphy was in the right place moments later though to put Town in front on 54 minutes, Skuse fed the ball forward, Pitman hooked it goalwards and Murphy stooped low to head in from a couple of yards.
Graham’s cross flew over the bar when he was in a great position before Wolves made a first change, Adam Le Fondre on for Edwards just past the hour.
Sears and Pitman linked up well down the left - not for the first time, Pitman’s cross just evading his on-rushing team-mate.
Ainsley Maitland-Niles replaced Bru in Town’s first change but on 74 minutes Wolves were level again, Le Fondre’s excellent cross headed in by Afobe.
The gold and blacks threatened again seconds later, Henry’s cross skimming across goal and just out of Le Fondre’s reach.
Maitland-Niles was agonisingly wide with a header from another excellent Sears delivery, while on the break Henry fired over.
Dean Gerken held firm from Le Fondre’s shot as the points hung in the balance, Sears showing great vision to almost release Knudsen inside the box.
Ikeme saved from Douglas after more clever play from Town, Kevin McDonald blasted over from 15 yards, then Douglas’ shot was blocked inside the box as Town were forced to settle for the draw.
Town: Gerken, Chambers, Smith, Berra, Knudsen, Skuse, Douglas, Bru (Maitland-Niles 68), Sears, Pitman, Murphy. Subs not used: Bialkowski, Malarczyk, Parr, Coke, Oar, Toure. Booked: Chambers.
Wolves: Ikeme, Iorfa, Williamson, Batth, Golbourne, Edwards (Le Fondre 64), Henry, McDonald, Price, Graham (Ojo 77), Afobe. Subs not used: Flatt, Doherty, Coady, Byrne, Holt. Booked: Le Fondre.