Devlin's strike sent Wellington into the break ahead, but the lead didn't last long, Jordan Mutch climbing between Phoenix defenders to meet a left-wing corner and plant a firm header past Oliver Sail early in the second half.
Hemed's moment came shortly after his introduction from the bench when Piscopo won Wellington a penalty and regular taker Davila allowed the Israeli to take responsibility, which he did with aplomb. But Western Sydney found a third equaliser less than sixty seconds later when Mitch Duke chested down a long pass on the edge of the area and swivelled to volley spectacularly past Sail, despite Phoenix protests about a push on centre-back Tim Payne as he leapt for the ball.
Western Sydney substitute Kwame Yeboah coolly put his side in front with six minutes left, but Hemed looked to have earned Wellington a share of the points in this extraordinary game when he lashed home in injury-time, only to see the goal chalked off by the VAR.
The game fell on the two-year anniversary of the Christchurch mosque shooting, with the home crowd impeccably observing a pre-match moment's silence. It was also exactly one year to the day since the Phoenix last played at Sky Stadium.
Wellington next face Brisbane Roar on Sunday, the first of three games in eight busy days.
Western Sydney Wanderers 4 (Wilmering 23, Mutch 52, Duke 65, Yeboah 84)
Wellington Phoenix 3 (Davila 7, Devlin 32, Hemed pen 64)