Showing no signs of fatigue following Tuesday's extra-time FFA Cup away win over Sydney FC and minus star striker Bruce Djite (calf), United bossed proceedings from the outset against a Glory outfit that had won their first two games.
Sergio Cirio and Awer Mabil were on target either side of half-time in a one-sided contest.
Cirio latched on to an exquisite throughball from Marcelo Carrusca to open the scoring in the 18th minute with a first-time finish.
The points were then sealed with 22 minutes remaining as Craig Goodwin surged forward before feeding Mabil, who cut inside and wrong-footed Perth goalkeeper Danny Vukovic with his cool finish.
Glory's best chance fell to Andy Keogh, scorer of a hat-trick last week, in the 37th minute, but he miscued a shot from close range.
Wellington Phoenix thumped Newcastle Jets 4-1 at Westpac Stadium in Sunday's other fixture.
Nathan Burns put the Phoenix in control with two first-half goals, before Michael McGlinchey made it 3-0 in the 64th minute.
Joel Griffiths' 90th-minute reply was nothing more than a consolation for the Jets and Wellington added a fourth through Andrew Durante in injury time.
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