A first-half Jeremy Brockie goal was enough to give Phoenix its first win of 2013 and drop Glory to last place.
After a cagey start by both sides at Eden Park on Saturday, it was Perth who created the first real opening.
A superb through ball from former Phoenix midfielder Nick Ward put Chris Harold clear.
The 20-year-old found himself one-on-one with goalkeeper Mark Paston but, under heavy pressure from the chasing Manny Muscat, he poked his shot wide.
Phoenix responded with two half-chances, with Stein Huysegems and Brockie both turning crosses past the post.
Brockie finally broke the deadlock in the 41st minute as he grabbed his 11th goal of the season.
After an elusive run by recruit Isaka Cernak, the ball went wide to Paul Ifill, whose cross was headed home at the far post by a diving Brockie.
The contest began to open up in the second half and Adrian Zahra came close to equalising for Perth, firing his shot straight at Paston.
Glory picked up the pace in the last quarter and substitute Ryo Nagai headed wide in the 79th minute.
Phoenix defender Ben Sigmund then pulled off a well-timed challenge to deny Harold a close-range shot at goal.
The home side did almost double the lead late on, with Ifill curling an effort just wide, but then had to overcome some further Perth pressure.
The match produced one setback for Phoenix, with Sigmund picking up another yellow card for a rash challenge on Harold, making him unavailable for the away match against leader Central Coast on Thursday.