Dani Sanchez shelled two good opportunities in the first half, but made amends in the 71st minute when his strike got Wellington back in the contest after they went 2-0 down with a quarter of the match left.
The Phoenix had to play the last 23 minutes with 10 men because Ben Sigmund was shown a red card for a mistimed tackle on Archie Thompson. Carlos Hernandez made no mistake from the penalty spot.
The dismissal means Sigmund will miss Friday night's home match against the Central Coast Mariners.
Phoenix skipper Andrew Durante cut a dejected figure after the game as he struggled to believe that his side couldn't take their chances against a Victory outfit who went through their first three games of the season without scoring.
"Melbourne were poor, we were very good and I'm still working out how we got nothing from the game,'' the defender said.
"We are playing some really good stuff. We were well on top and forced them into errors.''
Thompson put the Victory ahead after he grabbed the club's first goal of the campaign in the 42nd minute.
The well-placed strike came against the run of play after the Phoenix had the better of the opening exchanges but failed to take their chances.
Melbourne Victory coach Mehmet Durakovic was pleased to finally bag a win.
"It's not easy coming to Wellington and getting three points. But I thought the boys were willing and thoroughly deserved the three points,'' he said.
"We knew how they were going to come at us. The boys held off quite well in the first half and we managed to score so it wasn't a bad performance. But second half I thought we did quite well and got the three points.''
Much of the pre-game hype surrounded former Phoenix prodigy Marco Rojas' return to play in front of the Yellow Fever after he left Wellington to join the Victory at the end of last season.
But Durakovic benched the youngster and he didn't join the fray until the 64th minute where he was greeted with a string of boos.
The win leaves the Phoenix on four points from their first four games in a logjam in the middle of the ladder.