Tuipulotu's score helped give Scotland a narrow 7-3 lead at the break.
But second half-tries from Duhan van der Merwe, Josh Bayliss and Finn Russell put the result beyond doubt.
By contrast, Australia could only manage two Noah Lolesio penalties and debutant Harry Potter's converted try in reply.
Tuipulotu received the trophy from his Greenock-born grandmother -- through her he qualifies for Scotland -- after a team sponsor flew Jacqueline Thomson over from Australia to watch the match.
"It was an amazing moment," he told the BBC of collecting the trophy. "When she handed over the cup she said 'you got 'em!'"
The Wallabies came into this match on the back of last week's 52-20 rout of Wales, having launched their tour with a last-gasp 42-37 win over England.
Victory on Sunday would have left Australia coach Joe Schmidt, formerly in charge of Ireland, bidding for a clean sweep of wins over the Home Nations -- England, Scotland, Ireland and Wales -- against his old side in Dublin next weekend.
But Scotland, increasingly fluent in attack, ensured there would be no repeat of Australia's celebrated 1984 Grand Slam.
"I know everyone really wanted to be a part of a bit of history," Australia captain Harry Wilson told reporters. "It does hurt, but for us it's pretty exciting to get the opportunity against Ireland in six days' time."
Schmidt rued Australia's failure to take their chances and slack defending.
"You can't miss 30-plus tackles in an international against a really good team and expect to get the result at the end of it," said the New Zealander.
Victory meant Scotland ended their November campaign with the 'statement win' over a leading nation demanded by coach Gregor Townsend following this month's 32-15 loss at home to world champions South Africa.
'Found way to win'
Even so, Townsend was far from satisfied after Scotland's error-strewn opening 40 minutes.
"It shows we can get a win when we're not playing as well," he told the BBC.
"We're better than some of the aspects today, but I'm proud that the players found a way to win."
Australia, who had initially made six changes to the team that won in Cardiff, were forced into two more, with lock Jeremy Williams withdrawing through illness shortly before kick-off on Sunday, a day after hooker Matt Faessler was sidelined by a calf injury.
Despite the disruption, Lolesio's penalty gave Australia a 12th-minute lead.
Scotland, however, went 7-3 ahead in the 22nd minute.
A clever play saw hooker Ewan Ashman deliberately throw the ball over the top of a line-out to onrushing Melbourne-born centre Tuipulotu, who burst through Len Ikitau's attempted tackle for a try converted by playmaker Russell.
Tuipulotu, 27, was then involved in a collision with Joseph-Aukuso Suaalii that saw Australia's rising star leave the field.
"He's got a pretty numb arm, but we're hopeful it's not too bad," said Schmidt.
Russell's penalty early in the second half pushed Scotland 10-3 ahead.
A Scotland break-out move deep inside their own half led to an Australia drop-out from beneath the Wallabies' posts.
From the kick reception, Scotland worked an overlap in the 51st minute that allowed Van der Merwe to go over for his 30th try in 44 Tests as he regained outright the national try record from team-mate Darcy Graham.
Russell landed a tough conversion from the touchline and Scotland were well clear at 17-6.
Replacement flanker Bayliss then surged over in the 67th minute as he powered away from a trio of would-be tacklers.
Three minutes later, a slick move involving backs Huw Jones and Blair Kinghorn, allowed Russell to burst through from close range, with Potter's try too little too late for the Wallabies.
