Auckland striker Jesse Randall scored a brilliant individual goal in the 42nd minute of Saturday night's match at Perth's HBF Park to give the visitors the lead, and Glory looked bereft of answers until Kucharski entered the fray in the 59th minute.
The former Sydney FC striker scored the equaliser in the 75th minute when he controlled Scott Wootton's long ball with his thigh before dinking the ball over the advancing goalkeeper.
But the 23-year-old Kucharski saved his best for last, unleashing a 24-yard thunderbolt in the 90th minute to seal all three points for Glory.
The result lifted Glory (19 points) into ninth, just two points adrift of sixth spot, while Auckland, who started the round on top of the ladder, have now dropped to third on 25 points.
There was further bad news for Auckland, who lost New Zealand international Nando Pijnaker to a groin injury in the 27th minute.
And goalkeeper Oliver Sail, who had spent the previous two seasons at Glory before joining Auckland, had to be taken off on a stretcher in the 69th minute after injuring his left knee while taking a goal kick.
Sail, who was making his first appearance of the season, crumpled to the turf in pain after his knee twisted awkwardly, and the home fans chanted "you fell over" while he received medical treatment.
"I thought it was dislocated, but apparently it's a ruptured tendon," Auckland coach Steve Corica said.
"It's not great, to be honest with you. He will probably need an operation on that ... and will be out for a while."
There were very few highlights in the first half, and Auckland only had one wayward shot by the 42nd-minute mark before Randall changed everything with an individual piece of magic.
Randall tapped the ball forward into the box and used a burst of speed to round Will Freney before unleashing a low drive from a tricky angle to beat diving goalkeeper Matt Sutton.
It came in the same week Randall secured a deal to join Scottish Premiership club Dundee United at the end of the season.
But Glory finally came good late in the match, with Kucharski's double sealing the win and sending the 7528-strong home crowd into raptures.
"JK is a very good talent. We're very lucky to get him," Glory coach Adam Griffiths said of Kucharski, who only joined Perth this season after Western United were put into hibernation.
"I've been chasing him for since I've known him in the NPL, since he was 15.
"I'm very happy for him, you can see the qualities he has. And it's great that it came off."
23°C