A Macarthur clearance a minute after the restart cannoned against a Phoenix player into Hemed's path for a simple but composed finish — his sixth goal in five games.
Victory looked more likely once Macarthur's Loic Puyo was sent off for a studs-up tackle on Davila just before the hour mark. And the hosts were lucky not to be down to nine when Moudi Naijar escaped with a yellow card for a worse challenge on Clayton Lewis 20 minutes later.
The Phoenix should have scored several more in the second half — they hit the crossbar twice, had one cleared off the line and Hemed had his weak 85th-minute penalty saved by Adam Federici.
Their dominance was finally rewarded with a 92nd-minute goal from Ben Waine three minutes after getting off the bench.
So Wellington finish seventh, just a point behind Macarthur and Adelaide. Such a narrow miss would be frustrating for the Phoenix but in a season where they played just twice in New Zealand, they can be satisfied with such a strong finish — they earned 23 points from their last 11 matches after averaging just a point a game through the first 15 rounds.
Wellington Phoenix 3 (David Ball 45+1, Tomer Hemed 46, Ben Waine 90+2)
Macarthur FC 0