John van't Schip's side have lost just one league game since the turn of the year - a 3-0 reverse at Perth Glory on January 10 - and now sit only five points adrift of second-bottom Newcastle Jets.
David Williams again came off the bench to grab a late winner for ther Heart, just as he did in last week's victory over Sydney FC.
Patrick Kisnorbo gave Heart the lead six minutes after the interval at the Lavingdon Sports Ground, before Scottish midfielder Steven McGarry equalised on 73 minutes.
However, Williams had the final say with his 12th goal for the club eight minutes from time to give Van't Schip's men their third win in their last four A-League outings.
In Sunday's other fixture, Wellington Phoenix won a pulsating clash with the struggling Jets 3-2 at Hunter Stadium.
Phoenix went into the match with just one defeat in their last seven, and looked to be on course for another victory when Carlos Hernandez gave them a 21st-minute lead.
Craig Goodwin levelled with his first of the match shortly after, though, before Stein Huysegems restored Phoenix's advantage on 33 minutes.
Gooodwin again equalised early in the second half, but Jason Hicks' first goal for the club handed the visitors all three points.
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