The hosts won the toss and elected to bat first at the Gabba, but they looked to be in trouble when only Travis Head made it past the 20-run mark to leave Australia 78-5.
However, Glenn Maxwell steadied the ship with 60 runs from just 56 balls, before Wade helped Australia build a strong lead with an unbeaten 100 from as many deliveries - bringing up the century on the final ball of the innings.
The tail struggled to provide much support once Maxwell had been dismissed, but the hosts did manage to last until the end of the 50 overs, setting Pakistan a target of 269 to win.
The tourists, fresh off a 3-0 Test series whitewash defeat, struggled to get any sort of chase going, with James Faulkner dismissing the top order on his way to a four-wicket haul.
Mohammad Azam provided the best resistance with 33 off 46 deliveries, but the run-rate meant that Australia's target was never under serious threat and Pakistan were eventually bowled all out for 176.
The second ODI will take place at the MCG on Sunday.