Ernie Merrick's men missed the opportunity to close within a point of the top six after stumbling to a draw with the competition's cellar dwellers.
Cunningham looked at long odds of even playing in this encounter after injuring his foot during Wellington's last game, a 5-1 thrashing by Adelaide United.
But, despite initial reports he'd broken bones, the prognosis wasn't so bad for the Costa Rican striker who recovered in time to nod home the equaliser with five minutes remaining as Glory's defence eventually buckled.
Before that, the game had been a fairly forgettable encounter for much of the first 80 minutes.
Perth supporters would have hardly cared, though, as Glory opened the scoring through the unlikely figure of marquee man William Gallas in the 34th minute, the former French international side-footing home beyond Glenn Moss as the goal-shy club scored a first-half goal for the first time in nine matches.
Yet, last-placed Glory would soon be behind the eight-ball as injuries to Michael Thwaite (back) and Shane Smeltz forced the veteran duo off at half-time, leaving a very young Perth side out on the park - although they still appeared comfortably in control until their opponents lifted a notch in the last 10 minutes.
All of a sudden, Wellington were doing all the running and all of the attacking as Glory goalkeeper Jack Duncan, in his first start for the club following Danny Vukovic's shock loan-move to the J-League, was forced to save a one-on-one with Wellington's Roy Krishna.
Duncan was forced into action again soon after and was fortunate not to concede a penalty as he clashed heavily with Cunningham and may have even elbowed the striker in the head, with Cunningham's chipped effort just going wide.
Matthew Ridenton then missed a golden chance for the Phoenix as he spooned one over the bar from six metres before a last-ditch tackle from Perth's Matt Davies pushed a goal-bound effort from Stein Huysegems wide of the mark.
But Huysegems shot never went out and a desperate Tyler Boyd managed to keep it in play as his cross found Cunningham in close, the striker nodding a bouncing header past Duncan.
There was still time for Huysegems to see another headed effort deflected over the bar during injury time, but having failed to take that chance, Wellington had to settle for a share of the spoils.
The frantic closing stages were a far cry from an uninspiring first half where Perth controlled much of the possession.
Wellington still managed to create a good early chance as Krishna's powerful volley went wide, before Krishna also hit the post just before half-time as he was played in by a quality ball from Carlos Hernandez.
Hernandez wasn't to have his finest game, however, with the Costa Rican pulled from the ground midway through the second half, where he sulked on the bench and hit his hand against the dugout.