Fierce heat in Perth had initially threatened the game, with nib Stadium evacuated 90 minutes before kick-off due to a fire threat as temperatures touched 40 degrees Celsius
Play eventually did start on time, although the game was fragmented by drinks breaks in each half, with player safety at the forefront of the officials' thoughts.
It was the visitors who ultimately dealt best with the oppressive conditions, securing a third win over Perth this season, including last month's Westfield FFA Cup grand final.
All had not looked rosy for the Reds as Nebojsa Marinkovic fired the table-topping Glory into an 11th-minute lead after probing work from Andy Keogh on the left flank.
Glory were the architects of their own downfall, though, as goalkeeper Danny Vukovic invited Adelaide's strikers towards him before looking to catch them out with a quick throw.
However, the ball found Richard Garcia, whose miscued backpass found the now clear Craig Goodwin, who kept his cool and fired past the onrushing Perth goalkeeper.
Spurred on by their fortuitous equaliser, Adelaide dominated after the break and the winning goal arrived just three minutes into the second half, James Jeggo combining with Bruce Djite before smashing home from close range.
The Reds remain the only side to beat Glory this season and will head into the Asian Cup break just six points adrift of Kenny Lowe's side in fourth spot.
