Wade saved the Australian innings after the batting top order slumped to 78 for five after winning the toss.
Wade, who has been under pressure to score runs after a lean spell, turned the innings in a 82-run stand with all-rounder Glenn Maxwell and helped build the total with lower order partnerships.
He hit seven fours and two sixes in his knock for his first ODI century.
Maxwell was dismissed in the 31st over with Australia at 160 for six when he attempted to flick Hasan Ali over mid-wicket only to hit the ball with the high part of his bat and dolly an easy catch to Mohammad Hafeez.
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Mohammad Amir struck early with the key wickets of adventurous opener David Warner and skipper Steve Smith with successive balls to have Australian rocking at 13 for two.
Amir got one to straighten and Warner attempted to flick the ball into the leg side only to be bowled for seven.
Rizwan, deputising for first-choice keeper Sarfraz Ahmed who has returned home to tend to his seriously-ill mother, took a total of four catches in the innings.
Debutant Chris Lynn saw off Amir's hat-trick delivery and slammed a monster 97-metre six at his home Gabba ground in his breezy knock of 16 off 12 balls before he was caught behind off Hasan Ali.
Travis Head hit some delightful square and cover drives in his run-a-ball 39 before he was also caught behind of spinner Imad Wasim.
Hasan finished with the best figures of three wickets for 65 off nine overs.
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