Wicketkeeper Wade boosted Australia to 268 for nine off their 50 overs after the batting top order had slumped to 78 for five.
Seamer James Faulkner then took four wickets for 32 to help Australia dismiss Pakistan for 176 off 42.4 overs.
Pakistan were well placed with Australia five down in the 17th over before Wade and Glenn Maxwell (60) put on 82 runs for the sixth wicket to push on.
The tourists could not put any pressure on the Australians in their innings with skipper Azhar Ali injuring a hamstring and Babar Azam topscoring with 33.
"It was challenging at the top, it was swinging and seaming around," man-of-the-match Wade said.
"Maxi (Maxwell) took the pressure off me, and I was just looking to get him on strike. I was absolutely cooked (by the last over).
Wade, who has been under pressure to score runs after a lean spell, hit seven fours and two sixes in his knock for his first ODI century.
Maxwell was at his quirky best with reverse sweeps and improvised stroke-making in his 60 off 56 balls with seven boundaries before he was out to a false shot.
Pakistan soon struck trouble in their innings losing the free-scoring Sharjeel Khan for 18 off 22 balls, falling to Faulkner.
Skipper Azhar Ali injured a hamstring and retired hurt only to return in pain and try and help his side late innings before he became another Faulkner victim for 24.
"It's a bit sore, but hopefully it will recover soon," Azhar said.
Babar Azam, batting at No.4, topscored with 33 off 46 balls before he edged to Steve Smith at slip off Pat Cummins.
"We thought from five down for 78 we can get them out early, but unfortunately it didn't happen," Azhar said.
Smith said Australia paid for being in too much of a hurry at the top of their innings.
"It was a pretty average start. We were in a bit of a hurry, to be fair," Smith said.
"We bat all the way down. Mitchell Starc is batting at No. 10 at the moment. We've got a long order.
The second match in the five-ODI series will be played in Melbourne on Sunday.
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