American Baisden twice gave Glory the lead at No.2 Sportsground in Newcastle, the first time against the run of play, and she also hit the woodwork late in the game.
Newcastle have picked up four points from three games, two more than Perth.
Looking for their first win of the season, Perth continued their run of slow starts as Newcastle had 11 shots to two In the first half and the Jets were ultimately good value for their point.
The Jets lacked polish in the final third and Baisden made them pay just before halftime when Perth scored with their first on-target attempt.
Fellow American Cyera Hintzen swung across a fine ball from the left and Baisden finished in style at the far post with a fine close range volley.
Galvanised by the goal, Glory almost added a second on the stroke of halftime when Hintzen's 20-metre shot was palmed away by Jets goalkeeper Georgina Worth.
The Jets equalised in the 54th minute when Lauren Allan outmuscled Isabella Wallhead in a one-on-one contest for a through-ball and chipped over goalkeeper Sarah Langham.
The lead lasted just four minutes and Wallhead redeemed herself with a pinpoint cross headed in by Baisden.
Newcastle's Tara Andrews headed straight at the goalkeeper from close range, but substitute Ashlee Brodigan pulled the Jets level In the 77th minute when she slipped the ball past Langman.
Baisden almost completed a hat-trick and came close to winning the match for her side, but saw her powerful 80th minute shot crash against the crossbar, with substitute Alana Jancevski firing just wide in added time.
In the first half, Newcastle's Murphy Agnew and Lucy Johnson had shots saved and several other Jets attempts were blocked, but Langman was forced to push away a strong Tessa Tamplin shot from outside the penalty area.
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