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.
Although not quite the pyrotechnics that featured in the early part of Warner's career, there were seven boundaries in his 75-ball innings before spinner Sajid Khan trapped him in front with Australia 11 runs from victory.
A crowd of more than 24,000 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.
"It meant the world to me. I've given absolutely everything to play this game and to sacrifice a lot of things to be in the position that I am," Warner said of the ovation.
"I've had a lot of ups and downs through my career. I've had to come back and overcome adversity. I've done that, I think, very, very well. I think today just showed to me that I do have a lot of support, and I'm very, very grateful for that."
Warner's innings gave him a career tally of 8,786 test runs at an average of 44.59, making him the fifth most prolific Australian batsman of all time, behind Ricky Ponting, Allan Border, Mark Waugh and Steve Smith.
Marnus Labuschagne (62 not out) got the world test champions across the line with a single shortly after Warner's departure.
"It's gonna be hard to replace Davy," said Australia captain Pat Cummins, who was named Player of the Series for a 10-wicket haul in Melbourne and 5-61 in the first innings in Sydney.
"He's been such an integral part of every team that Australia has put out over the last decade. (Today) was a good reminder of what a high-class batter he is and how hard it's going to be to replace him. We're gonna miss him."
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.
On Saturday morning, 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.
Jamal was named Player of the Match for his bowling as well as his brilliant knock of 82 in the battling rearguard in the first innings that gave Pakistan a sniff of victory.
"We're learning the hard way," said Masood. "We have to take a lot of positives but we made a few mistakes that left the door open and Australia took full advantage of them."
