Defensive midfielder Ugarkovic bagged a quickfire double in the dying stages of the first half on Sunday to make light of City's missing attacking personnel.
Former Socceroo Andrew Nabbout and Marco Tilio were added to a growing injury list in last weekend's win over Western United.
In their stead 17-year-old striker Medin Memeti came into the side for his starting debut, along with forward Yonatan Cohen.
The last time these two teams met in the A-League, City conjured a remarkable 8-0 win in April.
Conversely, Perth defeated City 5-4 three months ago in a chaotic Australia Cup match-up.
This contest never threatened to reach those extremes, but City rarely looked anything other than routine winners at HBF Park against a Glory side that had conjured just one point and one goal in three outings.
City failed to convert a host of half chances during the first half, with Ugarkovic and Memeti going close.
It took a spectacular Ugarkovic strike from the edge of the penalty area six minutes from halftime to break the deadlock.
Five minutes later Ugarkovic doubled the advantage for the first brace of his eight-year, 225-match career.
City passed their way through a leaky Glory defence and Ugarkovic swept home with ease.
Matters went from bad to worse within 30 seconds of the second-half restart, with Andreas Kuen striking from distance into a partly unguarded net after goalkeeper Oli Sail's mishit clearance.
The Glory failed to put a shot on target until the second half, such was City's dominance.
It was always City that looked likely to add to the scoreline and sure enough Cohen netted a fourth six minutes from full-time with a confident left-footed low finish inside the far post.
City iced the cake in the dying minutes as a sweeping counter-attack ended with teenager Memeti finishing with ease for a maiden goal at professional level.
"We controlled the match really well, the first half was excellent and we created a lot of opportunities without the killer edge up front early on," City coach Aurelio Vidmar said after the match.
"The kids came on in the second half and had a bit of a crack, so really pleased with tonight."