Glory came into the clash with two losses and a draw in their last three outings but scored first through Adam Taggart.
They could have been more than a goal up and should have responded to the Sky Blues' reply from Alex Brosque.
Defender Marc Warren had three clear-cut first-half chances, two with the boot and one with the head, but couldn't force Danny Vukovic into a single save.
The Sky Blues took over in the second half with goals to Filip Holosko and Bobo before a Bernie Ibini penalty to remain unbeaten and seven points clear of Melbourne Victory in top spot.
As good as the goals were, nothing topped some of the saves from Vukovic highlighted by a remarkable effort to keep out a header from Perth skipper Rostyn Griffiths in the 65th minute.
Glory remain five points behind the fifth placed Brisbane Roar with three of their next four games away.
Stung by last week's disappointing home loss to Newcastle, Glory should have scored before eventually doing so in the 20th minute.
Warren couldn't capitalise on his chances but Taggart didn't miss from close range after good lead-up work by Brandon Wilson.
Immediately the Sky Blues responded and a final pass from Milos Ninkovic found an unmarked Brosque. He showed his class with a left-foot finish across Perth 'keeper Liam Reddy.
Things remained level until a pinpoint Brosque cross found Holosko at the back of the box in the 61st minute. His header was sublime and gave Reddy no chance.
A Griffiths header was on target for Perth but was denied by the hand of Vukovic, who quickly let teammate Michael Zullo know what he thought of his defending.
Sydney went up 3-1 when Bobo was found by a Ninkovic pass in the middle of the box. Perth's defence was poor and he capitalised to comfortably score in the 71st minute. Ibini then earned and scored the penalty to secure the 4-1 result.
