Returning Boro defender Stephen McManus put through his own net after 17 minutes although Grant Leadbitter soon levelled, his effort hitting the underside of the crossbar and adjudged to have crossed the line by the referee's assistant.
Boro hit the woodwork a total of four times in the first half but it was Wanderers who re-established their advantage immediately after the restart courtesy of the superb Bjorn Sigurdarson, yet once again Leadbitter pulled the visitors level shortly after with a great strike from distance.
Wanderers were applying plenty of pressure in search of a winner and Kevin Doyle sent the home faithful into raptures when he headed home in the 70th minute, inflicting an 11th league defeat on Boro in 14 games since the turn of the year.
Wanderers stopper Dorus De Vries was quickly called into action to save superbly from a sliced clearance by defender Kaspars Gorkss - setting the pattern for an impressive performance from the 'keeper.
A pulsating encounter flowed from end to end from the off and Wolves made the crucial breakthrough, Stephen Hunt getting down the left and firing in a cross which was diverted into his own goal by McManus.
But Boro were soon level in bizarre fashion. De Vries made a great parried save to deny Lukas Jutkiewicz, Leadbitter fired the rebound against the underside of the crossbar and - after another follow-up effort had hit a post - the assistant flagged to signal Leadbitter's effort had crossed the line.
Wolves needed just three second-half minutes to retake the lead, some well-worked play ending with Sylvan Ebanks-Blake backheeling the ball into the path of Sigurdarson, who raced past a defender before rounding Jason Steele and slotting home.
But Boro levelled once more, this time within four minutes, as Leadbitter's sweet 25-yard strike found the bottom corner.
The visitors twice cleared off the line before McManus got away with loud penalty appeals from the home side for handball, and Steele made a great save to deny Sigurdarson.
Yet Wolves did find a third in the 70th minute, Matt Doherty's long throw-in was flicked on by Roger Johnson and Doyle headed home.
Wolves were keen to see the game out after taking the lead for a third time and they did just that - much to the relief of the home support.