Maierhofer saw red after getting his second booking of the game for clattering into Tim Howard with only seconds remaining.
Kevin Doyle had put the visitors in front with 14 minutes left and it took until the last two minutes for Everton to break the resilient Wolves defence through Diniyar Bilyaletdinov.
The Toffees had the better of the early exchanges and came close in the 17th minute when Sylvain Distin's long ball forward was miscontrolled by Louis Saha and Tim Cahill picked up the pieces and smashed over from 12 yards out.
Saha had a chance from a Bilyaletdinov corner but the striker's powerful header was inches over.
Wolves defender Jody Craddock had to leave for stitches to a head injury after 20 minutes but soon returned sporting a bandage.
There was similar patching-up done by Wolves who worked their way back into the game and went close through Republic of Ireland international striker Doyle.
The best chance of the first half fell to Wolves striker Sylvan Ebanks-Blake who latched onto a low Ronald Zubar cross only to drag his shot on the turn just wide of Howard's goal.
It took only 25 seconds of the second half for the first chance to arrive when a Leighton Baines cross was met by Saha whose header was tipped over the bar by Wayne Hennessey.
Hennessey saved the day again on the hour mark when Bilyaletdinov was clean through for the Toffees but the Wales goalkeeper was more than up to the task.
Everton continued to press and Saha found space on the edge of the area before hitting a curling right-footed shot which Hennessey turned wide.
But it was Wolves who took the lead on 76 minutes when Doyle found himself one-on-one with Howard and slotted coolly home.
Everton threw everything at Wolves and were rewarded in the dying minutes when Bilyaletdinov smashed home at the far post from a Jo cross.
And the game looked to be heading for an uneventful finish until Maierhofer's sending-off for a reckless tackle on Howard.