The Wanderers had jumped out to an early lead thanks to a clinical counter-attack after McGlinchey's free-kick cannoned off the crossbar with Western Sydney goalkeeper Andrew Redmayne stranded. The ball fell favourably for the hosts, who capitalised on the Phoenix's high line to escape on a two-on-one break which saw Federico Piovaccari eventually roll it home into an empty net.
While the Wanderers' goal was opportunistic, the Phoenix responded with a rarity - a goal to Manny Muscat.
The Wellington left back nabbed his fourth goal in eight seasons with a curling right-footed low strike into the bottom left corner to level the contest against the run of play.
As a result of the Wanderers' weight of possession and territory, Phoenix goalkeeper Glen Moss was called into action several times before the half, sprawling in all directions to keep the hosts from going ahead again.
Moss was required less in the sloppy second spell, as his defensive backline put up a strong stand. As fouls and injuries contained the free-flowing nature of the contest, the Wanderers' accurate passing began to stray. As Western Sydney piled on the pressure, a mixture of fully committed blocks, tackles of brilliant technique and goalline clearances kept them at bay.
Skipper Andrew Durante was at the heart of the resolve, helped out by a fine performance by Justin Gulley and a committed cameo from Louis Fenton.
Just as they looked to have held on for a valuable road point, Bridge struck - the substitute crushing home an unstoppable strike after getting on the end of a corner at the far post.
The loss keeps the Phoenix in sixth spot on the A-League ladder, and they will now have to recuperate before their short turnaround, taking on Sydney FC next Thursday.