Heart had the first chance of the match, but it was Wellington who got the early goal as a counter attack allowed Roy Krishna to beat Patrick Kisnorbo as he moved the ball and slammed the ball under Andrew Redmayne.
Five minutes later Melbourne Heart thought they’d found an equalizer when Jonatan Germano headed home Ben Garuccio’s free-kick home, but he timed his run poorly as he was denied by the offside flag.
Heart had a good chance in the 15th minute as David Williams stole possession and fed Mate Dugandzic who could only blast it over the bar.
Melbourne Heart could well have lost Williams in the 17th minute as he blocked Krishna’s shot with his arm, but escaped the punishment of the referee.
At the half-hour mark Heart did have the equalizer as a clearance from a corner found Germano whose shot from distance hit the back of the net for a worthy equalizer.
Ben Sigmund hurt his team badly just after the goal as Sigmund challenged Williams twice, earning a yellow card for each challenge, to see Sigmund sent from the field of play, allowing Heart a golden opportunity to go for the win.
Despite being up a man towards the end of the half, Heart were unable to really have the desired impact as Wellington held on to go to the break on level terms.
Melbourne Heart nearly made it 2-1 just four minutes after the break as Dugandzic got through one-on-one with Glen Moss but was denied by a superb save from the Wellington keeper.
In the 56th minute Heart were punished for that missed chance as Krishna was able to send in a cross that Andrew Redmayne was able t parry away, but only as far as Terrance Boyd who sent the ball back across the corner.
Heart did manage to make the man advantage count in the 62nd minute after Harry Kewell was brought down by Manny Muscat, allowing Williams to make up for his miss by hitting the penalty home.
With the man advantage Melbourne Heart were always going to be the only side that could win the match and in the 80th minute they thought they did as Williams stuck the ball in to the back of the net but they were denied by the whistle for a high boot.
Melbourne Heart pushed hard to find a winner but they couldn't get the goal they needed and now sit six points adrift of Adelaide in sixth place, making their playoff chances very difficult.