Few teams put as many balls in to the penalty area from the flanks as the Phoenix do but it finally paid off when yet another cross in to the box saw Louis Fenton earn a penalty in the 66th minute and Brockie made no mistake with his spot kick.
With a vocal home crowd of 6410 behind them the Phoenix continued to press and Brockie nailed the go-ahead goal in the 71st minute when he was the first to pounce on a loose ball after a Dani Sanchez shot was deflected.
Phoenix coach Ricki Herbert said his side deserved the three points.
"Character's never left this team, I think that's really important to know. You can play all the fancy football and different styles in the world but this club's got some pedigree around that and I think that's served us in good stead in the past and will serve us well in the future,'' Herbert said.
"That was an important thing for me tonight that the character came to the fore in abundance when we needed it to so the performance came as well.''
The opening 45 minutes provided plenty of entertainment as the Heart opened the scoring with two early goals in the space of as many minutes and four players were shown yellow cards.
Firstly, Golgol Mebrahtu directed a gorgeous free kick in to the back of Mark Paston's net in the 14th minute after Phoenix skipper Andrew Durante had given away a foul at the top of the box.
The Heart then added to Durante's misery as a David Williams ball across the face of the penalty area struck Durante's foot and wrong-footed Paston and found it's way in to the Phoenix's goal only two minutes later.
The Durante own goal sparked the Phoenix in to life as they surged during a busy period that was capped off when Fenton pulled one back for the home side.
Heart coach John Aloisi was frustrated that his side dropped out of the contest so easily despite being 2-0 up.
"We started the game well and the first 15-20 minutes, [we scored] only two goals, but we were causing problems when we were going forward and finding good space and then we make a mistake and we just folded, the whole team,'' Aloisi said.
"Which is disappointing and then after that the Phoenix just dominated us and deserved to win the game and they were causing us all sorts of problems and we didn't keep the ball at all. We didn't keep possession after that and we didn't play ourselves back in to the game.''
The Phoenix's next game is against the Roar in Brisbane on New Year's day.
Wellington Phoenix 3 (Louis Fenton 21, Jeremy Brockie pen 66, 71) Melbourne Heart 2 (Golgol Mebrahtu 14, Andrew Durante og 16) HT: 1-2
