Having come back out for the second spell 2-1 down, the Phoenix had the better of the second 45-minute stanza but looked for long periods as though they wouldn't be able to find the killer blow.
Few teams put as many balls into the penalty area from the flanks as the Phoenix, but it finally paid off when yet another ball into the box earned Louis Fenton a penalty in the 66th minute and Brockie made no mistake with his spot kick.
With the momentum and a vocal home crowd of 6410 behind them, the Phoenix continued to press and Brockie nailed the winning goal in bizarre fashion in the 71st minute.
As a Dani Sanchez strike was deflected from long range, Brockie was first to pounce on the loose ball and the All White tucked it into the corner of Clint Bolton's net.
The opening 45 minutes provided entertainment as the Heart opened the scoring with two goals in the space of as many minutes.
Firstly, Golgol Mebrahtu directed a gorgeous free kick into the back of Mark Paston's net after Phoenix skipper Andrew Durante had fouled at the top of the box in the 14th minute.
The Heart then added to Durante's misery two minutes later when a David Williams ball across the face of the penalty area struck Durante's foot and wrong-footed Paston and found its way into the Phoenix's goal.
Wellington Phoenix: 3 (Louis Fenton 21, Jeremy Brockie pen 66, 71).
Melbourne Heart: 2 (Golgol Mebrahtu 14, Andrew Durante og 16). HT: 1-2
