Kristian Opseth scored one and set up two more as Carl Veart's side made it three games without defeat to move level on points with fifth-place Perth.
Riley McGree missed a 15th-minute penalty but the home side scored twice in two minutes through Michael Jakobsen and Lachlan Brook before the half-hour mark.
Kristian Popovic pulled a goal back but Opseth headed in Adelaide's third and teed up Ben Halloran to fire home the fourth before half-time.
Pacifique Niyongabire scored a fine first A-League goal, twisting and turning in the box before rifling in a shot, his stylish somersault celebration a fitting tribute to a thrilling game.
Bruno Fornaroli's fine turn and finish made it 5-2 and Juande scored from the spot in the 83rd minute, but Glory will be feeling the heat in the top-six chase after back-to-back losses.