Glory led 3-0 after 33 minutes of Sunday's match following goals to Kucharski, Kuzamba and the pink-haired Stefan Colakovski.
There could have been plenty more goals in the second half as Glory kept creating, but it wasn't until Matthew Ellis headed home in the 85th minute that Perth added the cherry on top of their impressive display.
The result left Adelaide with back-to-back losses to start the season, while Glory are one win and two defeats after three games.
United named a young starting XI featuring eight under-23 players given the club was playing their third match in the space of eight days, and with another AFC Champions League game in Singapore to come on Thursday.
Star Socceroo Craig Goodwin was absent due to personal issues, while Ryan Kitto and Juan Muniz were on the bench.
Adelaide looked flat from the outset, and it was a defensive howler in the 16th minute that gifted Perth their first goal.
After Adelaide goalkeeper Joshua Smits took some time to finally get his pass away, 18-year-old defender Feyzo Kasumovic inexplicably attempted a pass across the face of the box despite a number of Glory players being in the vicinity.
Kucharski reacted quickest to pounce on the rolling ball and bury his shot before Smits had time to scramble back to the centre of the goal.
Kuzamba almost netted his maiden A-League goal in the 15th minute when he found himself one-on-one against the goalkeeper.
That shot was saved but he nailed his next chance in the 20th minute.
Kuzamba passed to Kucharski and charged forward to receive the ball back before firing off his shot from a tight angle while falling over.
The 19-year-old lapped up the moment by unleashing a fly kick at the corner flag before celebrating with his teammates.
"This pre-season he's shown that he's got a really good physical profile," Glory coach Adam Griffiths said of 19-year-old Kuzamba.
"We've just asked him to attack. He had a one-on-one and then scored another. So he's getting into really good goal-scoring positions.
"But he's also got the ability to recover very fast, so he'll continue to grow and improve."
Things only grew worse for Adelaide, with Stefan Colakovski prodding home Glory's third goal from point blank range after gloveman Smits had been taken out while trying to save Cher Deng's header.
Colakovski was hard to miss given he had coloured his hair pink after hitting his goal of raising $10,000 during Breast Cancer Awareness month.
"I believe the three (first-half) goals we conceded were avoidable," Adelaide coach Airton Andrioli said.
"And then when you're 3-0 down so quick in the game, it changes confidence and belief in the players.
"But I didn't think we were playing a bad football match."
