Tony Popovic's men had the opportunity to move within two points of Brisbane Roar after the table toppers were held to a 0-0 stalemate at Perth Glory on Friday.
However, Marcelo Carrusca's fourth-minute strike proved enough for Adelaide at the Coopers Stadium, as Josep Gombau's side rose to fifth in the league.
Carrusca scored after Michael Zullo's fine run and cross from the left was not dealt with by Western Sydney keeper Ante Covic, and Bruce Djite squared to the Argentinian, who prodded home into the empty net.
The visitors came close to drawing level when Japanese playmaker Shinji Ono sent a bicycle kick over the bar on the half-hour mark.
But Adelaide were resilient at the back and held firm to extend their unbeaten run to six A-League games.
Western Sydney, meanwhile, have now won just one of their last five league outings.
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