The Heart, as usual, had their chances in front of goal but failed to put away a lacklustre Sky Blues outfit who were without striker Alex Brosque until late in the game.
Although the home side did force their former keeper Clint Bolton into a few vital saves, they were unable to hit the lead and unfortunately for them it was Melbourne substitute Adrian Zahra who was the man who broke the deadlock just five minutes from time.
The victory follows up the new A-League clubs 2-1 triumph over Adelaide United last Friday night and put them above derby rivals Melbourne Victory as the reigning champions joined North Queensland Fury on the bottom of the table.
Liam Reddy (gk), Stephan Keller, Hayden Foxe, Hiro Moriyasu, Bruno Cazarine (Danning 75’), Shannon Cole, Terry McFlynn, Mark Bridge, Scott Jamieson (Carle 60’) Sung-Hwan Byun, Dimitri Petratos
Subs - Ivan Necevski (gk), Nick Carle (60’), Kofi Daning (75’), Seb Ryall
Clint Bolton (gk), Michael Marrone, Simon Colosimo, Matt Thompson, Rutger Worm (Zahra 77’), Warne Srhoj, John Aloisi (Sibon 58’), Aziz Behich, Jason Hoffman, Josip Skoko, Nick Kalmar (Beauchamp 66’)
Subs - Peter Zois (gk), Gerald Sibon (58’), Michael Beauchamp (66’), Adrian Zahra (77’)