It was their largest win in terms of runs and their first Test series success against Australia since 1994.
The Australians resumed on 143-4 in search of an improbable 603 but lost their final five wickets for eight runs and were all out for 246.
Pakistan now move above England to third in the world Test rankings.
Pakistan won the first match in Dubai by 221 runs, which had been their previous record-winning margin in terms of runs against Australia.
The tourists lost only one wicket before lunch, but Steve Smith was lbw to the second ball of the afternoon session, just three runs short of a century.
Brad Haddin and Mitchell Johnson followed in consecutive overs with no addition to the total and left-arm spinner Zulfiqar Babar finished with 5-120, his second five-wicket haul in only his fourth Test, as Pakistan climbed three places to their highest ranking since 2007.
This latest defeat was Australia's 10th in their last 14 Tests in Asia.
Australia have a four-Test series against India at home next month, and co-host the World Cup with New Zealand in February and March before the Ashes series in England starting in July.
Pakistan recorded only their second Test series whitewash against Australia after winning by 356 runs on the final day in Abu Dhabi to seal a 2-0 victory.