Arsenal left it late as Henrikh Mkhitaryan came off the bench to rescue a point for the Gunners as he cancelled out Ivan Cavaleiro's earlier goal.
The Portuguese international capitalised on a Granit Xhaka mistake by playing a one-two with Raul Jimenez and calmly stroking the ball home.
Arsenal were lucky to be level as Mkhitaryan crossed into the box which evaded everyone and hit the back of the net before they rode their luck as Wolves had big chances to win in stoppage time.
A perfect game plan from Wolves
As Arsenal struggled to get going in the entire first-half Wolves were excellent and carried out a game plan to perfection as they got a goal early on.
Xhaka dummied the ball in his own half expecting a teammate to be behind him but it was Cavaleiro who latched onto the ball and drove at the Arsenal defence before playing a neat one-two with Jimenez and finishing past Bernd Leno.
The Gunners' only chance of the half fell to Alexander Lacazette as Mesut Ozil pulled the back to the Frenchmen who calmly took a touch to create space, but skipper Connor Coady was there as he rushed out to block the shot.
A constant threat on the counter
Wolves countered quickly afterwards as Helder Costa ran half the length of the pitch and managed to force a good save from Leno who got up quickly to stop Jimenez having an open goal.
As the game went on Wolves became more confident and Costa broke down Arsenal's left hand-side many times as Rob Holding couldn't deal with his pace.
Gunners sluggish in possession
It took until the 60th minute for the Gunners to register their first shot on target when Lucas Torreira hit a shot from 20-yards out after a short corner but Rui Patricio did well to tip the ball over the bar.
Arsenal managed to work a good opportunity to Hector Bellerin as Xhaka was played down the left and pulled the ball back to the Spaniard who had nobody around him on the penalty spot but couldn't even hit the target.
Bellerin was then again involved, receiving the ball with yards of space on the right-hand side of the Wolves box he perfectly picks out Pierre-Emerick Aubameyang but from less than 5-yards the Premier League player of the month managed to hit the post.
Late drama
As it seemed like Arsenal had wasted all of their chances for this game the substitute Mkhitaryan whipped in a hopeful cross which nobody managed to get a touch on and it drifted past Patricio who was helpless as he could only watch it hit the back of the net.
Arsenal were looking to steal three points in the final minutes but Adama Traore burst past Holding and cut back in the box and had a golden opportunity to send Wolves fans into delirium, but it was a poor effort by the Spaniard and he should have done much better.
In the final minute of stoppage time Traore showed his ability once more to get past his man and cut the ball back into the path of Morgan Gibbs-White who hit a curling effort from outside the box past Leno but it came off the bar and bounced on the line as Wolves went agonisingly close to reclaiming the lead and three points.