Seeking to arrest a two-game losing run on Sunday evening, the Jets took a 15th-minute lead through Xavier Bertoncello and looked to be in cruise control.
But Tom Lawrence's equaliser just before halftime snapped their momentum and with little more than 10 minutes remaining, an unfortunate handball from Daniel Wilmering allowed Nicholas Pennington to score from the penalty spot for the Glory's first win of the season.
The result moves the West Australians off the foot of the table, adding insult to injury, at the expense of the Jets.
Pushing numbers forward after a Perth turnover, the Jets started brightly when Alex Badolato slid a pass through Bertoncello to net the opener with his first ALM goal.
It threatened to open the floodgates, with another turnover moments later allowing Max Burgess to flash a shot wide.
Bertoncello forced a strong save from Matt Sutton in the 20th minute, and only desperate intervention from Brian Kaltack could stop Lachlan Rose from rounding the keeper and firing into an open goal in the 32nd.
But the Jets were punished for their wastefulness in the 38th minute when a turnover of their own allowed Rhys Bozinovski to seize possession and slide an inch-perfect pass through for former Rangers attacker Lawrence to finish.
The hosts were then dealt a sucker-punch in the 77th minute when, with Glory's first touch in their penalty area in the second half, Sebastian Despotovski headed the ball back into the arm of Wilmering, giving Pennington the chance to win it.
The Jets desperately tried to rally but after coming off the bench, Glory skipper Adam Taggart almost made it three instead - having a goal disallowed as well as hitting the crossbar.
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