The single competition point moved the Mariners up to third place, but it was an unconvincing performance by the defending A-League champions at home.
While the Heart's winless streak stretched to 18 games - the equal second longest in A-League history - they created more chances than the Mariners, who lacked creative spark without two key playmakers.
Marcos Flores suffered a season-ending knee injury during the week while midfielder Michael McGlinchey pulled out before the game with a virus in what was meant to be his last appearance before a loan spell at Japanese club Vegalta Sendai.
The Heart, whose A-League record of away matches without a win extended to 20, created almost twice as many goal attempts.
They spurned a fabulous opportunity in the 14th minute when Maltese striker Michael Mifsud struck the post from near the penalty spot after being put through by Harry Kewell.
On the stoke of halftime, Mifsud was unable to convert another cross from the lively Kewell, who played several dangerous balls into the penalty area through the game.
Heart's Iain Ramsay had a couple of decent shooting opportunities but blazed both over the bar, while Nicholas Kalmar shot straight at goalkeeper Andrew Redmayne.
The Mariners struggled to create chances, with fullback Storm Roux shooting straight at the goalkeeper in their only first half attempt on target.
They looked more dangerous in the second half, though the Heart continued to threaten.
Mariners fullback Josh Rose wasted the Mariners' best chance, blasting over from seven metres.
Nick Montgomery headed just wide from a Mile Sterjovski cross and Mitchell Duke sent a powerful late attempt just wide.