Playing her 90th match, Rigby broke the deadlock in the 54th minute on Sunday to put Glory on track for what would have been their fifth straight win.
But when Wanderers striker Sophie Harding was brought down in the box by Glory goalkeeper Morgan Aquino in the 80th minute, Amy Harrison stepped up to convert the penalty.
Glory striker Cyera Hintzen had the chance to win it in stoppage time when the ball sailed to her at the far post but hit the chance wide of the target.
The result reduced the gap between sixth-placed Glory and fourth-placed Melbourne Victory to four points.
Glory, who have five matches remaining, still have a game in hand on the defending champions.
But Perth will be left kicking themselves after letting points slip against the eighth-placed Wanderers, who kept their own finals hopes alive with a deserved point on the road.
The Wanderers had the better of the opportunities in the first half, firing 14 shots to five and enjoying 56 per cent possession.
Harding sent an early warning by striking the woodwork from long range in the second minute, and had another shot saved in the 29th.
Perth found their groove early in the second half, and it was Rigby who was the surprise goal scorer.
Rigby attacked a loose ball and completed a perfect one-two pass with Alana Jancevski before firing in her shot.
The game took another turn when Harding was brought down just as she was about to score.
The Wanderers converted the penalty, then survived a couple of late scares to secure the draw.
Western Sydney ended the match with 25 shots, but just three were on target.
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