Second-half goals to youngsters Terry Antonis and Blake Powell delivered a deserved win in front of 15,602 fans at Allianz Stadium.
The win ensured Sydney climbed to fifth spot, handing it some precious breathing room inside the top six with six regular season games to play.
The victory capped a memorable day for the club, after it announced the signing of Australia captain Lucas Neill for the rest of the season.
Despite a sense of optimism surrounding Neill's imminent arrival, and the midweek re-signing of coach Frank Farina, Sydney was slow out of the blocks.
However, it was clearly the better side by the time a dour, scoreless first half drew to a close.
Sydney lost Peter Triantis to a suspected knee injury after halftime and he was replaced by Paul Reid.
But it didn't stop the Sky Blues from coming to life as Alessandro Del Piero struck the left post with a curling, 30-metre free kick just minutes after the break.
It wasn't long before Sydney took the lead when Antonis struck in the 49th minute with his first A-League goal in 35 appearances for the club.
The midfielder collected the ball from Reid and there was more than a touch of fortune as his shot took a wicked deflection off Reds defender Iain Fyfe and went in.
Sydney kept up the pressure as Reid went close and the dangerous Del Piero forced a good save out of Eugene Galekovic.
But the goalkeeper was powerless to prevent Sydney's second goal in the 66th minute.
Adam Griffiths barged onto a Del Piero corner kick and Powell was there to clean up the scraps, turning the ball in from close range.
Adelaide kept the game alive when substitute Tomi Juric collected a Galekovic free kick and strode away to score.
There were some nervous moments for the home side, but it withstood some late pressure to seal a vital win.