Jamie Maclaren had given Perth the lead early in the first half, but Western Sydney hit back through debutant Liam Youlley in the second half.
A superb strike from Keogh on 66 minutes restored Glory's lead and sealed the 2-1 win, despite it going down to 10 late on after Denis Kramar was sent off.
The result pushed Perth to 50 points and trailing leader Melbourne Victory only on goal difference, however Glory's recent high-profile salary cap infringement means it will be relegated to seventh after the completion of this weekend's round.
The match was delayed for nearly an hour after Sydney was hit with a massive hail storm that covered the Parramatta Stadium pitch in hailstones.
Wanderers made six changes to the side that lost in Kashima midweek, with Youlley and Shayne D'Cunha making their starting A-League debuts.
The host had the better of play early on but it was Glory that came closest to scoring inside 10 minutes.
A deep cross was played to the far post and Rostyn Griffiths headed back across goal and onto the post. Richard Garcia attempted to head in the rebound from close range, but D'Cunha managed to block it on the line.
Glory continued to look dangerous on the break and went in front on 17 minutes.
Dino Djulbic played a perfect pass into the path of Maclaren, who burst into the penalty area and struck his shot low and into the far bottom corner to give the visitor a 1-0 lead.
Western Sydney's best chance of the first period came beyond the half hour. Kerem Bulut let fly from inside the area and Danny Vukovic managed to get down low and just keep it out before Perth's defence cleared away.
Glory made a blistering start to the second half. After the home side failed to clear a free kick, a Garcia header struck the bar and fell invitingly for Daniel De Silva.
In his last Perth appearance before leaving for Roma, the teenager inexplicably skewed his shot over from just metres out.
Despite creating little after the interval, Wanderers hit back on 53 minutes. A short free kick was squared to Youlley and his shot deflected its way past Vukovic pull the home side level.
Parity lasted only 10 minutes. Josh Risdon dribbled his way to the edge of the box and slipped a pass with the outside of his foot to Keogh.
The Perth striker nestled his first-time shot into the bottom corner to restore the visitor's lead.
Wanderers received a boost in the final 20 minutes when Gol Gol Mebrahtu came on as a substitute to make his long-awaited return from injury.
Perth was forced to see out the remainder of the encounter with 10 men after Slovenian Kramar was sent off for a second bookable offence after clumsily brining down Bulut.
Western Sydney was unable to take advantage of the extra man as Glory held on for a 2-1 win.
