Craig Goodwin's 23rd-minute strike was the difference between the two sides, with victory leaving Adelaide a point behind Central Coast Mariners in the race for second place.
The Roar had a golden chance to level from the penalty spot six minutes before half-time, but Joseph Champness' effort was kept out by a low save from James Delianov after Ryan Kitto handled in the area.
Sydney FC and Macarthur are level with Adelaide on 35 points as the season nears an exciting climax.
Brisbane remains in sixth, the final quarter-final place, despite its defeat as seventh-placed Western Sydney Wanderers was thumped 5-1 by Perth Glory.
The Glory prevailed thanks to a masterclass from Andy Keogh, who scored four goals for Perth to move them three points behind Brisbane. Joel Chianese rounded out the win deep into injury time.
The day's other game saw Wellington Phoenix go within three points of the Roar as it held league leader Melbourne City to a 2-2 draw.
Jamie Maclaren's free-kick nine minutes from time put City 2-1 ahead to seemingly secure maximum points, only for Tomer Hemed's second in the 88th minute to ensure a share of the spoils.