The two teams went into the game locked in seventh place, level on points on goal difference, but the Heart now leapfrog city rivals Victory into fifth place, leaving the Phoenix lowly in eighth.
The Phoenix started brightest on a sunny afternoon, with the first 15 minutes belonging to the away team, but the Heart began to come into their own as the half wore on. Tony Warner was forced to produce a stunning save to keep the game scoreless after Ben Sigmund was caught in possession, diving to tap a Rutger Worm volley around his right post.
The Heart enjoyed large periods of possession and they made their dominance count five minutes before the break.
Melbourne captain and former Phoenix midfielder Fred took a quick free kick near halfway, releasing Worm into the Phoenix box. His shot cannoned off Warner's right post and the ball fell kindly for Mate Dugandzic to tap in his fourth goal of the season.
Melbourne struck the post again right after halftime and the lucky let-off appeared to spark some urgency among the Phoenix. Coach Ricki Herbert changed things up by introducing Mirjan Pavlovic in place of Nick Ward, before Dani Sanchez returned from injury for his first appearance for the Phoenix since the loss to Central Coast in early November.
The moves brought about the best spell of the second half for Wellington, with Sanchez immediately showing what they have been missing.
His cross was diverted onto the bar by Heart defender Adrian Madaschi with 25 minutes left, before the woodwork was again rattled a short time later.
A teasing Ifill run was halted illegally by Madaschi just centimetres outside the penalty area and, from the resulting free kick, Sanchez was desperately unlucky not to mark his return with a goal. He curled the ball cleanly around the wall but the right post came to the aid of Bolton.
The Phoenix had another great chance to steal a point with five minutes left, with Sanchez again at the centre of the action. He looked to have slid a shot past Bolton in goal but a Heart defender came to the rescue and deflected the ball behind.
Melbourne Heart 1 (Dugandzic 41) Wellington Phoenix 0. HT 1-0.