David Warner was denied the chance to score the match-winning runs in his final test but contributed 57 as Australia cantered to their target of 130 runs to beat Pakistan by eight wickets and sweep the series 3-0.
Pakistan, looking to end a run of 16 successive losses in Australia since 1995, had added 47 runs to their overnight tally at the cost of their final three wickets, to be dismissed for 115 an hour before lunch.
Playing his 112th match before retiring from the format, Warner shared a hug with opening partner and childhood friend Usman Khawaja at the boundary rope and was given a guard of honour by the tourists as he came to the crease.
Khawaja departed lbw for a duck in the opening over, but Warner played like a man on a mission and was soon cutting the ball through the covers in trademark style for his first four.
He brought up his 37th test half century with a single to square leg, and Australia went to lunch with the win all but in the bag on 91/1, 39 runs from their target.
There were seven boundaries and a couple more chances in Warner's 75-ball innings before spinner Sajid Khan trapped him in front with Australia 11 runs from victory with a day to spare.
A crowd of more than 22,000 at his home Sydney Cricket Ground rose for a final ovation as Warner left the field, his part in the 2018 ball-tampering scandal that earned him a one-year ban from international cricket forgiven.
Warner's innings gave him a career tally of 8,786 runs in 112 tests at an average of 44.59 with 26 centuries since his debut against New Zealand in 2011.
Marnus Labuschagne (62 not out) got the home side across the line with a single shortly after Warner's departure.
As in the second test in Melbourne, Pakistan had only their own batting frailties to blame for missing out on the chance to snap their long losing streak in Australia.
They were looking good to set their hosts a far more imposing target on a deteriorating pitch before Josh Hazlewood (4-16) took three wickets in the penultimate over of the day on Friday.
Mohammad Rizwan scored 28 before he was caught by Warner off the bowling of Nathan Lyon with Aamer Jamal holing out for 18 three balls later. Hasan Ali was bowled by Lyon for five to end the innings.
Seamer Jamal, who took a six-wicket haul on debut in the first test in Perth and another in the first innings in Sydney, was not brought on to bowl until after lunch in a baffling decision by captain Shan Masood.
Reuters