Shannon Cole's first-half strike gave the visitors all three points, taking them two points clear of Brisbane Roar, who have a game in hand.
Heart enjoyed plenty of posession, and they pushed hard for an equaliser, but they were ultimately left to rue missed chances, with substitute Mate Dugandzic seeing his late header come back off the crossbar.
Cole struck the game's only goal in the 27th minute, as Adam D'Apuzzo's ball in from the left channel split Heart's defence.
D'Apuzzo almost found the head of Aaron Mooy, but the partial clearance only went as far as former Sydney FC man Cole, who - at the second attempt - powered a strike past a hapless Andrew Redmayne.
Heart had enjoyed plenty of possession in the opening quarter-hour, with Golgol Mebrahtu influential with a physical presence in the final third.
Mebrahtu had two sights on goal in the opening two minutes, but typical of their season - and what would also ensue over the remaining 88 minutes - they could not find the decisive finish to kick-start their 2013-14 campaign.
Dugandzic went closest late in the game, his header coming back off the crossbar and sparking a goalmouth scramble, but John Aloisi's men were out of luck as the ball stayed out.
Western Sydney striker Tomi Juric should have sealed the result for his side with time running out, but a brilliant save from Heart goalkeeper Redmayne kept him at bay.
The result leaves Heart with just two points from the first five games of the season and rock bottom of the table, as they extended their own unwanted run to 10 matches without a win.
