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.
The deadlock was broken in the 25th minute by one of the strangest goals of the season. Davis returned Carl 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 Hunt.
Ikeme, heavily involved in the freak opener, was then withdrawn at the interval by Saunders to be replaced by Dores De Vries.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.
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.