The Gunners were heading towards a first defeat since the opening fortnight of the season, only for Henrikh Mkhitaryan's fortunate late goal to make it three Premier League draws in a row.
Ivan Cavaleiro had edged Wanderers in front 13 minutes into the contest, and the visitors can consider themselves unfortunate not to have left the Emirates Stadium with all three points.
Arsenal's slow start to the match was punished 13 minutes in by Cavaleiro, who picked up the ball in central midfield after Granit Xhaka let it roll right past him, before exchanging passes with Raul Jimenez and tucking past Leno.
That goal marked the first time that Wanderers had ever taken the lead in a Premier League game with today's opponents - a run spanning eight matches.
The Gunners finally appeared to spark into life with over a quarter of the contest played, but Wolves quickly countered from Alexandre Lacazette's blocked shot and should have had a second.
Helder Costa was kept out by Leno inside the box and the German goalkeeper quickly pounced on the loose ball to prevent Jimenez from firing home.
Leno also had to be alert to keep out another Costa attempt later in the half, this time from the edge of the box, while Jimenez fired a shot wide after making the most of a scuffed Shkodran Mustafi clearance.
Having been brought into the starting lineup as Arsenal's only change from their last league outing, taking over from the benched Mkhitaryan, Alex Iwobi was sacrificed at the interval for Matteo Guendouzi.
The change in setup did not initially have the desired effect, as it took until the hour mark for Arsenal to register their first on-target attempt through Lucas Torreira's long-ranger.
Arsenal, for all their possession, struggled for ideas and did not create another opening until 18 minutes from time when Hector Bellerin guided a shot over the crossbar from a good position.
Bellerin then picked out Pierre-Emerick Aubameyang in the middle, but the Gabonese striker could only turn the ball onto the post from six yards.
Then came a pivotal moment in the match as, moments after Diogo Jota had missed a glorious opportunity at one end, being denied by Leno when picked out at the end of a counter, fellow sub Mkhitaryan found the net at the other.
Arsenal worked a short corner to Mkhitaryan, whose intended cross went right the way through and into the far corner of the net without any further touches.
Unai Emery had Leno to thank for taking a point from the match, though, as the summer signing thwarted Traore from a one-on-one position in added time, before Gibbs-White sent a first-time shot against a combination of the post and crossbar in a frantic finale.
ARSENAL (4-2-3-1): Leno; Bellerin, Holding, Mustafi, Kolasinac (Mkhitaryan 76'); Torreira, Xhaka; Iwobi (Guendouzi 46'), Ozil (Ramsey 75'), Aubameyang; Lacazette
WOLVERHAMPTON WANDERERS XI (3-4-3): Patricio; Bennett, Coady, Boly; Doherty, Moutinho, Neves, Jonny; Costa (Traore 75'), Jimenez (Gibbs-White 85'), Cavaleiro (Jota 61')