While they had crisscrossed Australia — from Sydney to Perth to Tasmania and back to Sydney in the past seven days, Adelaide have had two trips to Sydney since the start of this month.
That has to make a difference — and probably did in the first half especially — as the Phoenix struggled to hold possession.
With their third match in seven days, coach Ufuk Talay shuffled his team, with Joshua Laws and James McGarry coming into the backline for Steven Taylor and Sam Sutton.
Cameron Devlin was swapped out for Alex Rufer, while Hemed had a first start for four games.
After a stirring rendition of the Last Post and both national anthems, the Phoenix made a swift start, as a Waine header struck the crossbar in the second minute off a Davila cross.
The home team dominated the opening stages, and Adelaide keeper Joe Gauci did well to save point blank from Davila, after the Mexican was clean through on goal.
As the visitors got into their rhythm — with their neat passing game — they monopolised possession for the rest of the half, though couldn't create much, while the Phoenix were restricted to counter-attacks, as they sat back in a compact formation.
Adelaide were transformed after the break. Craig Goodwin dragged wide from a rebound, when it looked easier to score, before Stefan Mauk finished a wonderful passing move to give the South Australian side the lead in the 51st minute.
Two vital interventions from Sail kept them in the game, before some magic from Davila created the equaliser. His precise through ball was deflected into the path of Waine, who rounded the keeper and finished with aplomb.
Waine became only the fourth Phoenix player, after Jeremy Brockie, Roy Krishna and Ulises Davila, to net in four consecutive games.
Another top-class save from Sail kept the scores level, though Josh Cavallo should have buried the rebound.
David Ball, Clayton Lewis and Davila had late chances, before Hemed looked to have settled it, but his instant volley off a Louis Fenton cross shaved the post.
The game looked headed for a draw before Hemed's late penalty after a foul on Jaushua Sotirio by Gauci.