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The result sent almost all of the 7,548 spectators home happy and also puts the West Australian side equal top of the Hyundai A-League after three rounds.
It was Heffernan’s first goal in a Glory shirt, while Mehmet, again standing in for Shane Smeltz, notched his second of the season having scored on the opening day against Brisbane Roar.
It took ten minutes for the first real chance of note when a cross from Josh Risdon found Heffernan alone at the back post, but his volley was parried by Clint Bolton and the follow up was cleared off the line by Patrick Gerhardt.
Heart registered their first shot on goal on 16 minutes when a scuffed free kick by David Williams was attacked by Fred but his sliding effort went harmlessly over.
The visitors struggled to get their passing game going with a number of loose balls costing them possession in the final third, though Scott Jamieson was forced in to a last ditch challenge in the area to deny Mate Dugandzic.
Glory were described as being ‘over physical’ in some quarters during the week, and Steve Pantelidis did his best to live up to that reputation with a crunching challenge to win the ball against Williams.
Jamieson was proving a threat for Glory with his left wing crosses and deliveries from dead balls, but it was a Liam Miller corner which finally led to the first goal on 38 minutes.
The delivery was low to the near post but Michael Marrone only connected with fresh air in his attempt to clear and Heffernan was on hand to turn the ball home from six yards. The home side nearly doubled their lead right on half time but Billy Mehmet was inches away from connecting with another dangerous Risdon cross.
Heart suffered a blow when an eye injury to skipper Fred forced them into a half time substitution, Josip Tadic his replacement.
Both sides had early chances, with Steven McGarry firing over from inside the area for Glory and David Vrankovic volleying across goal from Dugandzic’s free kick at the other end. Travis Dodd began to cause problems with his direct running, and his cross set up Mehmet who headed wide from a good position.
The winger then tried his own luck but shot tamely at Bolton after twisting and turning inside the box. Glory substitute Chris Harold looked lively when he came on and almost made it two as he raced on to a ball from Mehmet but his shot went over.
The second goal arrived just minutes later when once again a Liam Miller corner was turned home, this time by the head of Mehmet.
Heart were poor for most of the game and failed to really test Vukovic in the second half, with Glory more than deserving of the three points.
Perth Glory: 1. Daniel VUKOVIC, 4. Billy MEHMET, 5 Steve PANTELIDIS, 7. Jacob BURNS, 8. Dean HEFFERNAN, 10. Liam MILLER, 13. Travis DODD, 14. Steven MCGARRY, 19. Josh RISDON, 21. Scott JAMIESON, 23. Michael THWAITE.
Subs: 6. Nick WARD, 11. Adrian ZAHRA, 17. Chris HAROLD, 20. Lewis ITALIANO (GK).
Melbourne Heart: 1. Clint BOLTON, 2. Michael MARRONE, 5. FRED, 6. Patrick GERHARDT, 8. Matt THOMPSON, 9. Dylan MacAllister, 11. Richard GARCIA, 15. David WILLIAMS, 16. Aziz BEHICH, 18. David VRANKOVIC, 23. Mate DUGANDZIC.
Subs: 10. Josip TADIC, 17. Jason HOFFMAN, 20. Andrew REDMAYNE (GK), 21. Steven GRAY.