Nicolas Pepe had handed Arsenal a deserved lead after Mikel Arteta's side dominated the early openings of the contest, with Bakary Sako hitting the post and having a goal ruled out for offside.
The game turned on it's head on the brink of half-time. David Luiz trip on Willian Jose in the penalty area resulted in a straight red card for the defender before Ruben Neves comfortably converted from the penalty spot.
Joao Moutinho's first goal since 2019 put Wolves ahead four minutes into the second half, prior to Bernd Leno receiving his marching orders for denying Adama Traore a clear goal-scoring opportunity by using his arm outside the penalty area.
The victory hands the Wanderers their first three points since they defeated Chelsea in December, whilst Arsenal fall to defeat for the first time in seven.
Story of the match
Nuno Espirito Santo tinkered his formation again, opting for the back four to face Arteta's side. However his choice nearly came back to haunt him when makeshift left-back for the night Max Kilman, had the ball played over him for Bukayo Sako to smash the ball against the post after only 35 seconds.
Wolves failed to react to the early opportunity for the 19-year-old and the winger had another chance to score three minutes later, but Rui Patricio was quick to deny him.
It did seem third time lucky for Saka when he fired Alexandre Lacazette's cut-back into the corner of the net, but VAR was on Wolves' side to rule the goal out for offside.
The disallowed goal did wake the Wanderers up, with Kilman heading over from a Moutinho cross before Nelson Semedo was denied his first Wolves goal by Leno.
Arsenal made their dominance pay shortly after the half-hour mark when dispossessed Semedo before jinxing past Neves and curling the ball into the net.
The goal is the Ivory Coast international's fourth league goal of the season and his second in consecutive league games after finding the net at Southampton last week.
Wolves were handed a double lifeline in the closing stages of the first half as Luiz was shown a straight red card for bringing down Jose in the penalty area. Referee Craig Pawson showed no hesitation and pointed to the penalty spot.
Neves, who recently missed the Crystal Palace defeat, tucked the penalty away to level the scoring and turn the game completely around for the second half.
Arteta's response to his side going a man down and seeing their lead taken away from them was to introduce Gabriel into the center of defence, with Lacazette coming off.
The substitution hardly helped Arsenal, with Emile Smith-Rowe playing the closest to a striker and Granit Xhaka having to assist the front three when going forward.
Wolves certainly had the momentum at the start of the second half and they took the lead when Moutinho's brilliant left-footed strike arrowed past the helpless Leno, off the post and into the net for his first goal since November 2019.
Things went from bad to worse for Arsenal when Leno was shown a straight red card for handling the ball outside his area and denying Adama Traore a clear goal-scoring opportunity.
Runar Alex Runarsson came on with 15 minutes to go for his first taste of Premier League action following his summer move from Dijon FCO.
Wolves dominated in the final quarter of an hour, with Jose missing Traore's header and Pedro Neto stinging the palms of Runarsson. Pierre-Emerick Aubameyang had the Gunners' only chance of the second half, but his effort from Hector Bellerin's cross was superbly blocked by Conor Coady.
Back four did well
When the game was 11 v 11 prior to Luiz and Leno being sent-off, Wolves did seem shaky at the back, but the extra man going forward certainly helped when they attempted to counter-attack Arsenal.
The front four of Daniel Podence, Neto, Traore and Jose certainly looked dangerous in attack and they all played a big part in turning the game around in the second half.
Jose, despite not finding the net, will be happy with his contribution and effort at Molineux, certainly showing the qualities that Wolves have been missing since Raul Jimenez's injury.