The win kept Perth's lead down to four points from second-placed Wellington Phoenix and Adelaide is now only six points behind the leader in third place after 14 rounds.
It was Adelaide's third victory over Perth this season. The Reds beat Glory 2-0 in their prevous league match and also prevailed 1-0 in the FFA Cup final.
The game was pushed back from 5pm local time to 5.30pm but that made no difference with the temperature 39 degrees at kick-off and still 35 at full-time.
Despite that conditions the Reds showed its attacking intent early and Argentine playmaker Marcelo Carrusca had two scoring chances inside three minutes.
First he burst through Perth's defence but he was stopped by an immaculate tackle from Josh Risdon.
Then he played a vicious cross that had Danny Vukovic in all sorts of trouble but the ball caressed the crossbar before it was cleared.
However Perth went ahead in its first attack in the 11th minute when Andy Keigh set up Nebojsa Marinkovic on the edge of the penalty area and the star midfielder picked his spot and beat goalkeeper Paul Izzo with an angled low drive.
Keogh underlined his and his team's confidence by trying an outrageous lob from just outside the centre circle that finished just over the bar to the relief of Izzo.
Adelaide did not offer much in terms of response. The Reds managed to hold the ball longer than their opponent but Perth was more dangerous in its fewer attacks.
Glory however gifted Adelaide an equaliser on the half hour when Richard Garcia tried to pass the ball back to Vukovic but he inadvertently served the lurking Craig Goodwin who had no difficulty in steering the ball home for the softest of goals.
The unexpected goal gave Adelaide a new lease of life and James Jeggo tested Vukovic with a low shot that the goalkeeper saved well.
Moments later Bruce Djite broke free in the penalty area but Garcia made up for his earlier error by making a vital tackle when the striker was about to pull the trigger.
Adelaide dominated the latter stages of an entertaining first half despite the prevailing heat and Vukovic deprived Djite again after the striker made space for himself and fired strongly at goal but the goalkeeper was well positioned to block the shot.
Garcia went close with a header soon after the restart before Adelaide took the lead when Djite set up unmarked Jeggo who expertly planted the ball home past Vukovic's reach.
Adelaide's passing game continued to improve as the game wore on and Sergio Cirio, who had a quiet game, burst into life on 75 minutes with a mazy run that ended with a rising shot that clipped the upper part of the bar and bounced to safety.
Substitute Jamie Maclaren had a chance to pinch a draw for his side when he tried a lob from distance but the ball missed the bar.
