The opening spell was a largely forgettable 45 minutes as both sides misfired in front of goal.
Phoenix striker Jeremy Brockie skewed the first chance of the game in the eighth minute when he beat the offside trap but couldn't get any power or direction behind his shot, which set the tone for the first half.
Wellington midfielder Carlos Hernandez hit the post only a couple of minutes later before Kenny Cunningham then put a header from a Hernandez free kick straight in to the arms of Heart custodian Andrew Redmayne.
Heart striker David Williams made a meal of a great opportunity in the 20th when his shot at an open goal went wide as Phoenix goalkeeper Glen Moss breathed a sigh of relief.
The sound of the referee's whistle was a constant as the game lacked structure and Melbourne found a surprising amount of space down Wellington's left side, where Phoenix defender Manny Muscat was given a stern examination.
Muscat, who earlier today signed a two-year contract extension with the club, was his typically-abrasive self during the first spell as he looked to get involved from left back.
The second stanza brought much of the same, although both sides enjoyed their own patches of dominance in what was a more evenly-contested half.
Wellington's defence, anchored solidly again by skipper Andrew Durante, proved resolute as they withstood Melbourne's advances and the Heart struggled to connect on their chances at goal.
The game was in desperate need of a goal and the deadlock was finally broken in the 75th minute when substitute Tyler Boyd delivered a low cross in to the box and the hard-working Stein Huysegems scored from close range.
It marked the second week in a row the former Belgian international had got on the score sheet after his strike was the difference in Wellington's 1-0 win over Sydney FC at the Cake Tin last weekend.
Boyd nearly won a penalty for the visitors with about five minutes left but Wellington's appeals for a spot kick were waved away.
With both coaches having emptied their benches there was plenty of energy during the final stages but neither side could find another goal.
Wellington may have a slight concern on the injury front as right back Louis Fenton came off late in the game after he appeared to suffer another knock to the shoulder he dislocated during the pre-season.
Wellington Phoenix 1 (Stein Huysegems 75) Melbourne Heart 0 Halftime: 0-0
