Pakistan, trailing the three-match series 1-0 after losing the first match in Sharjah by 93 runs, were put on course for a big total by openers Sarfraz Ahmed (65) and Ahmed Shahzad (61).
But Australia pulled back through Mitchell Johnson who took 3-40 in his 10 overs.
Asad Shafiq (29) and Fawad Alam (20 not out) laboured in the final overs before they were bowled out in 49.3 overs.