Keogh scored the first goal of the contest in the 15th minute on Saturday night before setting up the second in the 63rd minute that ensured Glory remained unbeaten under new coach Tony Popovich.
While Keogh didn't score the second, his shot needed to be saved. Then the rebound off Roar keeper Jamie Young was hammered into the back of the net by Brisbane defender Connor O'Toole.
There were nervous moments late when Adam Taggart converted a penalty for Brisbane against the side he left in the off-season.
Perth were down a man too after a red card to Tomislav Mrcela but held on for a second win of the season to go with a draw. Brisbane is winless with a loss and two draws.
It was all Glory early on and the home side had two clear cut chances to score on the one attack, but both headers from Keogh were spectacularly saved by Young.
Keogh had another chance in the 15th minute and didn't miss this time. A perfect set up cross from Chris Ikonomidis only needed a Keogh tap in and Young had no chance this time.
That proved the only score of the opening half before Glory went up 2-0 in the 63rd minute.
A Scott Neville pass put Keogh in a good position to get off a shot. Again it was well saved by Young but that went straight to O'Toole, who only managed an own goal.
Brisbane kept coming and eventually Taggart was brought down in the box by Mrcela.
Taggart scored from the spot to the boos of his old fans but he didn't celebrate, while Mrcela's night was over.
They couldn't find another, though, with Glory doing enough for the win.
