The success was Wade's first televised title since he won the 2021 UK Open. Klinge, playing in only his second World Series event, averaged 104.56 in defeat.
Wade broke early in the final with an 11-darter to lead 2-0, but Klinge responded with a 12-dart leg to level at 2-2.
Wade then took four legs in a row, including a hat-trick of 13-darters, to open a 6-2 lead. Klinge won three consecutive legs, landing a 140 checkout, to close to 6-5, before Wade took out 76 in the 12th leg and punished two missed doubles from his opponent to seal the win.
Wade had earlier recovered from 5-2 down against Stephen Bunting in the quarter-finals, hitting a 164 checkout on his way to a 6-5 win, before defeating top seed Gerwyn Price 7-4 in the semi-finals with eight maximums and an average of just over 101.
On Friday, he had averaged 112.73 in a 6-0 opening-round win over Tim Pusey.
Klinge reached the final with wins over Ross Smith, Gian van Veen and Jonny Clayton. The Australian saved two match darts before beating Smith in a deciding leg in the first round, then knocked out world number two Van Veen in the quarter-finals.
He averaged almost 102 in the semi-finals against Clayton, taking out 170 to end the New Zealand Masters champion's bid for back-to-back Oceanic titles.
"It's been a while since I've won something," said Wade. "My children always say to me: 'Daddy can you get a trophy?' I have to keep buying them. I really enjoyed myself this weekend, and to win the title in Australia is even better."
Klinge said: "It's been absolutely amazing. The crowd have been behind me the whole time and I've really enjoyed the whole experience. Every opportunity that comes my way I'll try and take it."
In the other semi-final, Clayton had beaten Australian number one Damon Heta 6-3, while Price reached the last four with a 6-2 win over Josh Rock.
The World Series of Darts Finals conclude the season in Amsterdam, with a 32-player field competing at AFAS Live from September 17th to 20th. Six-time champion Michael van Gerwen will aim to retain the title, with world number one Luke Littler also in the field.