English striker Adam Le Fondre's 37th-minute goal decided the cagey contest and put the Sky Blues five points ahead of third-placed Melbourne Victory.
Sydney will clinch second with a round to spare if defending champions Victory don't win at Adelaide on Friday.
Perth coach Tony Popovic made six changes to his starting side following last week's Premiers Plate-clinching win.
The Glory didn't have a single shot on target, although they pressed hard in the closing minutes without creating too many clear-cut chances.
Sydney had a few more opportunities, but the league's two meanest defences held sway for most of the match.
Le Fondre couldn't miss his chance as he was virtually standing on the line, when Paulo Retre's header from Anthony Caceres' cross flicked off him.
It was the former Premier League striker's 16th goal of the season, taking him one clear of Wellington's Roy Krishna in the Golden Boot race.
It was Sydney's only shot on goal in a tepid first half, with marquee Siem de Jong's 25-metre shot thudding into the Glory wall.
Veteran striker Brendon Santalab had Perth's only attempts of note in the first 45 minutes, heading wide and then firing a strong long-range shot just off target
In the second half, Retre, Rhyan Grant and Brandon O'Neill all had shots for a livelier looking Sydney and half-time substitute Diego Castro added some pep in attack for Perth.
Near the end, Popovic gave his 17-year-old son Kristian his A-League debut off the bench.