Australia won the toss and chose to bat in scorching conditions amid talk their stacked line-up - including Big Bash League sensation Chris Lynn at number four - would lead to a T20-style encounter.
However, they were reduced to 5-78 after just 17 overs.
Mohammad Amir clean-bowled Warner (7) and then handed captain Steve Smith his first ODI golden duck in successive deliveries, meaning Lynn faced a hat-trick ball on debut. He survived, but not for long - two overs after sending Hasan Ali into the grandstands, he totally misread a slow ball and skied one behind to Mohammad Rizwan.
It was left to Wade and Glenn Maxwell (60) to rescue the innings with a crucial sixth-wicket partnership of 82, scoring at nearly a run a ball.
Maxwell was making his return to the Australian side after he was controversially dropped and fined last month for saying it was "painful" having to bat below Wade in the Sheffield Shield.
This time he batted above him, and if there were any residual problems between the pair, they weren't showing.
Wade was more than happy to turn the strike over to Maxwell, who smacked seven boundaries and injected some much-needed life into the Australian charge before holing out to Mohammad Hafeez.
Still, it was a timely knock from the 28-year-old ahead of Sunday's announcement of the squad that will embark on a four-Test tour of India next month.
Wade eventually brought up his century with the final ball of Australia's innings, and only after some comical running between the wickets with Australia's tail-enders.
Australia's other debutant, Billy Stanlake, finished on 1 not out but bowled only three overs and spent most of the evening off the ground due to sickness.
Pakistani commentator Waqar Younis was full of praise for the Aussies' redemption, applauding Matthew Wade's superb innings and the bowlers' clever use of pace.
"It's an unbelievable win for the Aussies. Full credit to the way they used the bat and ball, especially Wade," he said.
