Sydney hit the lead in the 23rd minute on Saturday when Kyah Simon struck a sweet goal while falling to the ground.
But two goals to Di Bernardo either side of an Alanna Kennedy own goal saw Perth take complete control.
And with Sydney chasing the game, Glory striker Rosie Dee Sutton and Shawn Billam put the icing on the cake with late strikes in front of 1592 fans.
Canberra United will host defending champions Melbourne City in the other semi-final on Sunday, with the winner of that match to meet Glory in the title decider on February 12.
Sydney FC had the better of the early running, and Simon gave the visitors the perfect start.
Star Glory winger Sam Kerr was a constant threat.
But it was Di Bernardo who levelled the scores via the penalty spot after Alyssa Mautz was brought down in the box in the 29th minute.
The turning point of the match came in the 58th minute when Kennedy's attempt at a defensive clearance went horribly awry.
Kennedy could only look on in horror as her scuffed clearance looped over goalkeeper Claire Coelho and into the back of the net.
Di Bernardo scored her second goal with a sweet left-foot strike in the 77th minute.
And two minutes later Dee Sutton got onto the scoresheet when she nailed home a goal after Kerr's shot was saved.
But the best strike of the day belonged to substitute Billam, who nailed a stoppage-time goal from outside the box with a perfectly-struck floater.