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The home side started brightly, and midway through the first half, they opened the scoring when Hernandez converted from the penalty spot.
Phoenix continued to dominate as the match inched closer half time and doubled their advantage through Cunningham, who powered into the penalty area before curling a right-foot shot into the corner.
Wellington appeared to be coasting to the three points after pushing Adelaide onto the back foot for the majority of the second half, but Mabil bundled the ball home in added time to ensure a frantic finish.
However, time quickly ran out for the visitors as Wellington moved above Newcastle Jets in the standings.