Hazlewood, O'Keefe take three wickets each as Misbah’s men are bowled out for 244 in Sydney
Pakistan was bowled out for 244, shortly before tea on the final day, falling well short of the target of 465.
Josh Hazlewood and Steve O'Keefe took three wickets each, while Nathan Lyon took two and Mitchell Starc pitched in with one.
Sarfraz Ahmed, the Pakistan wicketkeeper, made a fighting, unbeaten 72 off 70 balls, but as wickets fell around him, the visiting side could not hold out for a draw.
Australia had won by 39 runs at the Gabba and an innings and 18 runs in Melbourne. The home side consolidated its second place in the ICC Test rankings, while Pakistan slipped to fifth.
It was Pakistan's 12th straight defeat in Australia since its last Test win in Sydney in November 1995.
David Warner, who made a scintillating hundred before lunch on the opening day and backed it up with the second-fastest fifty ever in Tests in his second hit, was player of the match. Steve Smith, the skipper, was player of the series for his 441 in five innings at an average of 110.25.
Pakistan began the day at 55 for 1, but Australia chipped away.
Azhar Ali, the side’s best batsman of the series, lasted just six balls into the final day and couldn’t add to his overnight score of 11, giving Hazlewood an easy return catch. He finished with 406 runs at 81.20, the most runs for a Pakistani in a series in Australia.
Babar Azam followed him back in Hazlewood's next over, trapped leg before wicket for 9.
Younis, the first-innings centurion, missed out on becoming the first Pakistan batsman to reach 10,000 Test runs when he was caught in the deep off Nathan Lyon for 13.
Nightwatchman Yasir Shah's 93-ball defiance ended half an hour before lunch when he was snapped up by fielding substitute Jackson Bird off O’Keefe, the left-arm spinner, for 13, as Pakistan went to lunch with half their line-up dismissed.
Asad Shafiq and Misbah-ul-Haq, the captain, added 40 for the sixth wicket, before Shafiq fell soon after lunch, bowled by Starc for 30.
Sarfraz then joined his captain in a partnership of 52 runs. Misbah had resisted for 98 balls before he went after O'Keefe and was caught by Lyon at mid-off for 38. It was his highest score in the series.
O’Keefe had both Wahab Riaz and Mohammad Amir sent back, before Hazlewood claimed the last wicket, of Imran Khan, to wrap things up.
Australia tours India next month for a four-Test series, while Pakistan will go to the West Indies for a four-match series in April.