David Davis scored a freak own goal to give the rock-bottom visitors a first-half lead and the Robins looked on course for their first away win since Sean O'Driscoll took charge.
But Sylvan Ebanks-Blake and Kevin Doyle converted two Stephen Hunt crosses to earn just their second victory in 2013 and end a seven-game winless run at home.
A tense start to the match between teams separated by just goal difference ahead of kick-off saw few chances. Steven Davies fired wide after racing clear of the Wolves backline and no-one could get on the end of Doyle's low cross at the other end but the strugglers were cancelling each other out.
There was then a delay while the injured Paul Anderson was taken off and replaced by Albert Adomah, who was unlucky not to start the match having shone in the win over Middlesbrough.
The deadlock was broken in the 25th minute by one of the strangest goals of the season. Davis returned Ikeme's short goal-kick back to his goalkeeper but the ball went straight through his legs and into the back of the net. It was not a strong backpass but on target - which meant Ikeme's miscontrol proved costly.
The shell-shocked Molineux fans saw their side create the next real chance and only a fantastic block from Liam Fontaine denied Doyle the equaliser. But their attempts at a leveller before the break were not helped by two enforced changes, David Edwards and Bakary Sako being replaced by Bjorn Sigurdarson and Stephen Hunt.
Adomah, arguably City's man of the match last time out, was next to threaten but his effort was blocked by Roger Johnson.
The final chance of the match saw Ebanks-Blake fire over the crossbar with a 20-yard effort after Doyle had knocked the ball into his path.
Ikeme, heavily involved in the freak opener, was then withdrawn at the interval by Dean Saunders to be replaced by Dores De Vries. That change meant the former Doncaster boss had used all his three substitutes after just 45 minutes.
Doyle, who scored twice when the sides met earlier in the season, had the first chance of the second half after a goalmouth scramble but he fired wide from six yards out.
At the other end De Vries was involved for the first time on the hour mark but he made a routine save from Davies' long-range shot.
Four minutes later City had Tom Heaton to thank for keeping their lead intact. The former Cardiff shotstopper pulled off a top-drawer save to keep out Ebanks-Blake's 18-yard effort.
Wolves have not won a Championship match this season when conceding the first goal and Sigurdarson in particular was doing his utmost to change that with a number of opportunities.
And they drew level with 14 minutes to go when Ebanks-Blake span and volleyed Hunt's pass into the top corner.
The game was then turned on its head just four minutes later when another Hunt delivery allowed Doyle to head home a goal at the near post for a goal which could prove priceless for Wolves.
- Sports & Recreation
- Kevin Doyle
- Stephen Hunt