The win sees the Reds leapfrog Sydney into fifth spot on the table and leaves the Sky Blues with just four points from their last six matches and in danger of falling out of the six.
United put on a dominant, purposeful performance in the opening period with the attacking philosophy of coach Josep Gombau evident throughout.
They dominated possession and looked to push the ball forward at every opportunity.
In contrast, Sydney looked directionless for large periods of the opening stanza, and while they were still able to create several chances, they were left to rue their inability to finish in front of goal.
In the 17th minute the visitors had the opener through Bruce Djite. A perfectly weighted long ball put Marcelo Carrusca into space down the right and he turned his defender before finding Djite with a clever pass.
Fresh from notching his 100th A-League appearance last week, the striker was able to create separation from his defender and calmly slot the ball into the bottom right hand corner to give the visitors the lead.
They almost doubled their lead minutes later when only a last ditch clearance off the line by Matthew Jurman denied Tarek Elrich after his goal-bound shot got past Sydney keeper Vedran Janjetovic.
After 27 minutes, the Reds did have their second when a long clearance kick left Fabio Ferreira one on one with half the field to work with.
Ferriera brought the ball down neatly before outrunning the defender and firing past Janjetovic to give Adelaide a two-goal lead at the break.
The second half produced a better response from the home side, and they created some clear-cut chances, but they were unable to convert any of these and the frustration grew as the half wore on.
This was made worse 10 minutes from time when Adelaide put the game to rest.
A defensive error saw the ball fall to the visitors and a clever through ball put Sergio Cirio through on goal.
Cirio unselfishly put the ball across the face of goal where it was met and finished at close range by Jeronimo Neumann.
Sydney FC 0
Adelaide United 3 (Djite 17, Ferriera 27, Jeronimo 79)
Crowd: 13,335 @ Allianz Stadium
