The eighth-seeded Shelton crunched 19 aces, the third-fastest serve of the tournament and never even offered up a single break point in ousting Sweeny 6-3 6-2 6-2 on Thursday.
Averaging an ace and a half every game and dropping only five points after landing his first delivery, Shelton barely gave the Australian underdog a look-in on John Cain Arena.
Despite never really standing a chance, Sweeny through himself around the court and dived for volleys like vintage Boris Becker at the net in pursuit of another boilover after ending Gael Monfils' AO career in round one.
"Dane is a great competitor, a really tough guy to play. He's electric," Shelton said.
"It's clear why the Aussie crowds love him here and he's a fan favourite and I'm sure he's going to be lighting up John Cain (Arena) for many years to come.
"This is a court that I'm experienced playing on. I'm experienced playing Aussies here. I'm sorry about the outcome today, but I love the chants. I love the noise.
"I love the passion that you guys have for the sport. So thanks everybody for coming out today, even if you wanted me to go down."
Despite his exit, Sweeny will depart with a cheque for $225,000 after winning three matches to qualify, then claiming his maiden main-draw win at a slam.
The 24-year-old is also set to soar 34 spots up the rankings to a career-high No.148 in the world.
Shelton, meanwhile, marches on and next plays fellow Valetin Vacherot in the third round after Monaco's 30th seed eliminated Sweeny's fellow Australian Rinky Hijikata 6-1 6-3 4-6 6-2.
Fifth seed Lorenzo Musetti also advanced to the last 32 on Thursday with a 6-3 6-4 6-4 win over fellow Italian Lorenzo Sonego.
Musetti awaits the winner of 11th-seeded 2023 Open finalist Stefanos Tsitsipas and Adelaide International winner Tomas Machac.
Russian world No.18 Karen Khachanov beat American qualifier Nishesh Basavareddy 6-1 6-4 6-3.
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