The Glory took the lead via Susan Phonsongkham in the 12th minute on Saturday before Emma Robers scrambled an equaliser 10 minutes later.
But Jancevski's magnificent set piece proved the difference, handing United just their second defeat of the season, before recruit Hannah Blake added a third in the 96th minute in Ballarat.
The newcomers remain top of the table on 27 points, ahead of Melbourne City (25) and Sydney FC (24) while Perth sit sixth on 12 points, nine behind fourth-placed Victory but with two games in hand.
Perth broke the deadlock from the penalty spot after Phonsongkham went on a mazy run through the six-yard box and was brought down by Mel Taranto.
The young midfielder stepped up and converted by steering it into the bottom corner.
Glory goalkeeper Sarah Langman made an incredible save to deny Robers in the 15th minute and two minutes later Mel Taranto skimmed a shot over the bar.
Perth equalised when golden boot leader Hannah Keane, teammate Danielle Steer and Langman all collided mid-air in an aerial duel and the ball fell to Robers, who had the presence of mind to cooly smash it home first-time.
Both Keane and Langman required treatment but recovered.
United goalkeeper Hillary Beall made a superb save to deny Phonsongham a second in the 28th minute.
Keane had a great chance to hand Western the lead when she burned off multiple defenders in the 52nd minute but hit a tame shot straight at Langman.
Eight minutes later, Jaclyn Sawicki forced a superb leaping save from Langman.
But it was Perth who had the last laugh.
Jancevski brilliantly curled an unstoppable free kick past Beall to restore their lead.
Then, with almost the final kick of the game, Isabella Foletta pulled off a magnificent through-ball, which a bursting Blake met then coolly slotted home to seal three points.
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