The home side took the lead in the 13th minute through a lucky Dyron Daal goal before the visitors went on a spree, scoring three goals within 14 minutes at the start of the second term.
A late Ufuk Talay penalty gave the Fury hope but the Heart held out for another good result on the road which allowed to go fifth on the table and take their unbeaten streak to six matches.
GOAL The Fury struck first in the 13th minute when Panny Nikas’ free-kick from outside the area came off the shoulder of Dyron Daal with the deflection sending Heart keeper Clint Bolton the wrong way to get the home side off to the perfect start.
The Fury had a few strong chances after their opener but were a little sloppy in the forward third just as the Heart were in defence.
Melbourne did manage to come into the match as the first half went on but were unable to get a shot on goal and needed to completely change their game around in the second 45 minute spell.
GOAL The visitors got the equalizer they yearned for just five minutes into the second term when Rutger Worm played a lovely one-two with Gerald Sibon down the right flank before the Dutch winger slotted a nice ball in front of teenage striker Eli Babalj, who came on in the first half, and he finished neatly past Justin Pasfield to square it up at 1-1.
North Queensland looked threatening for a patch before the Heart grabbed their second through Sibon. GOAL The big Dutch striker got on the end of a Pasfield clearance by flicking the ball up to himself before using his backheel to turn his defender and then placing it past the Fury keeper to make it 2-1, forcing the home side to drop their heads.
GOAL And before too long, Melbourne had a third when Wayne Srhoj pounced on a Mark Hughes error in midfield before taking the ball into the area and cutting it back for Adrian Zahra who only had Pasfield to beat and he did it calmly for his first A-League goal.
The Fury kept pressing for a second to give them some hope and it came in the 85th minute when Heart substitute brought down Daal in the area. Fury skipper Ufuk Talay stepped up to the penalty spot and put it away in the top left corner but he had to take it again as a bunch of players had encroached the line.
GOAL On his second attempt, Talay went the same side but this time along the deck and Bolton was none the wiser as he went to his left for the second time.
The dynamics of the game changed yet again but the Fury were unable to force a draw and would have rued that fact considering at one stage they were in complete control.
Justin Pasfield (gk), Brad McDonald, Mark Hughes, Gareth Edds, Dyron Daal, David Williams, Panny Nikas, Chris Grossman (Talay 72’), Chris Payne (Spagnuolo 72’), Osama Malik, Isaka Cernak (Sipi 65’)
Subs - Sebastian Usai (gk), Lorenzo Sipi (65’), Ufuk Talay (72’), Jason Spagnuolo (72’)
Clint Bolton (gk), Michael Marrone, Michael Beauchamp, Matt Thompson (Colosimo 68’), Rutger Worm (Terra 78’), Gerald Sibon, Wayne Srhoj, Aziz Behich, Josip Skoko, Nick Kalmar (Babalj 37’), Adrian Zahra
Subs - Peter Zois (gk), Eli Babalj (37’), Simon Colosimo (68’), Alex Terra (78’)