Captain Aaron Finch smashed 55 and anchored Australia to 163-7 with five balls to spare as Ben McDermott flicked Haris Rauf to backward square leg for a boundary.
Aaron Finch hit a half-century as Australia won the series 2-1 but lost the three-match Test series 1-0.
Babar Azam top-scored for Pakistan with 66 off 46 balls while Hasan Ali conceded 30 runs off his three overs without taking a wicket.
Babar Azam struck six fours and two sixes in his 46-ball half-century for Pakistan before being caught off a short ball by Adam Zampa.
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