In a match played in driving rain, the Glory were second best for much of the contest but took the lead through leading scorer Andy Keogh just after half-time.
The Jets wasted a host of gilt-edged chances throughout the contest and were made to pay as Glory substitute Nebojsa Marinkovic sealed the visitors' win with a thumping strike in the final 10 minutes.
Keogh's 50th-minute opener saw him plant a close-range header past Ben Kennedy from Jamie MacLaren's cross.
And Keogh was also involved in Perth's second goal as he flicked a long ball into the path of Marinkovic, who found the net with a rasping drive.
Perth are now level on points with leaders Melbourne Victory, while the Jets remain rock-bottom.
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