They played with freedom and enterprise for good chunks of the game, inspired by the talismanic Paul Ifill, who found gaping holes in the Heart defence, and the suddenly in-form Leo Bertos.
Stein Huysegems was also involved in much of the play, though he rather blotted his copybook by receiving a second yellow card and missing the final seven minutes of the game.
The Heart, winless in 15 games on the road, barely threatened the Phoenix goal, and the result could be damaging to their playoff hopes.
The Phoenix made a cracking start to the game and should probably have been three or four goals to the good by halftime.
Three early corners were followed by a Brockie shot that grazed the crossbar.
Brockie provided a lovely cross for a Huysegems header that also hit the crossbar, and from a free kick, defender Ben Sigmund had a great opportunity but his header bounced up and over the bar.
A goal seemed inevitable and arrived in the 19th minute. Ifill, holding the ball up well on the left, sailed in a delightful ball for the in-form Brockie to score.
It should have been 2-0 just three minutes later but Husyegems, one-on-one with Heart keeper Andrew Redmayne, hit the left upright with his shot.
The second half featured far fewer highlights, though Ifill produced one trademark moment of brilliance when he stepped, cut and unleashed a powerful shot that would have been worthy of a goal. Replacement Louis Fenton also had a golden opportunity to score an insurance goal in the final minute but he blazed over the bar.
Wellington Phoenix 1 (Jeremy Brockie 19), Melbourne Heart 0. HT: Phoenix 1-0.
