In front of a bumper crowd at Forrestfield United's splendidly-appointed Hartfield Park ground, Kenny Lowe's men fell behind to an Angel Andres goal before Taggart restored parity on 36 minutes.
And despite creating a flurry of chances in the final 20 minutes, Glory were unable to secure the victory.
There were, however, plenty of positives to come out of the game, notably another eye-catching midfield performance from Mitch Nichols, an accomplished display from Scott Neville in the unaccustomed role of centre-back and some flashes of brilliance down either flank from Joel Chianese and Daniel Stynes.
Glory very nearly broke the deadlock within the opening 60 seconds as Taggart was denied at close range by a superb reflex save from Ryan Montgomery and the Socceroos striker went close again moments later, dragging his shot across the face of goal after being played in by Nichols.
In a lively opening, Liam Reddy was called into action at the other end to keep out a well-struck effort from Rhys Loxley, but the Glory 'keeper was powerless to prevent the State Team from taking the lead on 18 minutes.
Dianella White Eagles forward Andres found a pocket of space on the edge of the box and turned cleverly before rifling a shot into the net.
Glory took some time to recover from the setback, but when they did muster a response, it was a stylish one.
Chianese was the architect, beating two men in a slaloming run down the right and feeding Taggart who calmly found the bottom corner.
Tempers then frayed shortly before the interval after David Perich thuindered a free kick straight at Callum Timmins and in the ensuing fracas, Andy Keogh was cautioned.
Lowe's men started the second half as brightly as they had the first, with Shane Lowry heading a Stynes corner against the bar six minutes in and Taggart and Stynes both drawing saves from substitute goalkeeper, Jason Saldaris.
Luke Bodnar and Taggart were next to test the overworked Saldaris as Glory pressed for the winner in the final quarter and Keogh also went close to converting a fine, low cross from Bodnar.
Substitute Joe Knowles then cut in from the left but fired over the bar with 12 minutes left and the State Team duly negotiated the final moments to secure a share of the spoils.
WA STATE TEAM 1 (Angel Andres 18') PERTH GLORY 1 (Adam Taggart 36')
WA STATE TEAM: 30. Ryan MONTGOMERY (1. Jason SALDARIS 45'), 12. Alex CASTIELLO (4. Jesse FULLER 55'), 3. Chris SALDARIS, 20. Daryl NICOL, 18. David PERICH (13. Scott BULLOCH 55'), 6. Matt NTOUMENOPOULOS (7. Scott WITSCHGE 63'), 13. Nathan COSTELLO, 2. Nathan SMITH (5. Steve PURTON 63'), 14. Paul LLOYD, 17. Rhys LOXLEY, 15. Angel ANDRES (9. Richard HOWLES 55')
SUBSTITUTES NOT USED: None
PERTH GLORY: 33. Liam REDDY, 23. Scott NEVILLE, 3. Marc WARREN 4. Shane LOWRY, 5. Luke BODNAR, 6. Mitch NICHOLS, 7. Joel CHIANESE (26. Jacob ITALIANO 80'), 24. Callum TIMMINS, 9. Andy KEOGH, 22. Adam TAGGART, 25. Daniel STYNES (19. Joe KNOWLES 67')
SUBSTITUTES NOT USED: 13. Nick FEELY, 8. Jack LEECH, 15. Hayden STEVENS, 27. Riley WARLAND