The Gunners had led twice through Folarin Balogun, but Wolves fought back with goals from Bruno Jordao and Perry late on.
Wolves had made the worst possible start against a strong Arsenal side at Telford, as Balogun slotted his side in front after just 40 seconds.
However, the first-half was much more even than it appeared it would be at that point, and Wolves asked questions of their visitors.
Lewis Richards passed up the best opportunity, firing Jordao’s cross over at the back post after good work by Oskar Buur down the right.
Arsenal’s danger was coming through Balogun, who raced through with half-time approaching, only to be denied by Andreas Sondergaard, who made himself big to save.
After the interval, Wolves impressed and Perry was denied by a fantastic Karl Hein save, before Jordao was sent through and calmly slotted in at the near post for 1-1.
Jordao almost had a second soon after too, side-footing over the bar, before the Gunners retook the lead as the ball fell nicely for Balogun inside the Wolves area and the striker rifled home his second of the night.
However, Wolves fought back for a second time at the death to earn a deserved point as Elliot Watt brilliantly found Perry, who guided home with seconds remaining.
COMING UP
Wolves begin their Leasing.com Trophy campaign on Tuesday evening with a trip to League Two Carlisle United.
NEXT FIVE
24/09 Carlisle United (A) LCT
27/09 Southampton (H)
01/10 Morecambe (A) LCT
20/10 Liverpool (A)
26/20 Tottenham (H)
TEAMS
Wolves: Sondergaard, Buur, Sanderson, Marques, Kilman, Richards, Perry, Watt, Samuels (He), Jordao, Shabani.
Unused subs: Cristovao, Nya, Taylor, Dai.
Arsenal: Hein, Bellerin (Swanson), Tierney (Omole), Burton, Clarke, Mavropanos, Coyle, McEneff, Balogun, John-Jules, Tormey.
Unused subs: Hillson, Smith, Bola.
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