De Minaur's triumph made him the youngest victor of the Sydney tournament since his mentor Lleyton Hewitt claimed it as a 19-year-old in 2001.
Barty, who was runner-up in the Sydney final on Saturday night, weathered on early storm from Thailand's Luksika Kumkhum before winning 6-2, 6-2 in the night session on Margaret Court Arena.
Regardless, it showed world No.15 Barty is ready to challenge anyone at next week's Australian Open.
Seppi was again the first to strike in the second set.
"I've got a lot of expectations now".
Last year Barty won two WTA titles, reached the fourth round at the U.S. Open and earlier this week beat world number one Simona Halep in Sydney.
"I think once you start thinking in different ways to deal with these situations, that's the wrong thing to do", he said.
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"To back it up from Sydney, I am proud that I was able to get it done in three sets."
Thompson, 24, had broken his teammate's serve early in the second set, but it was not enough to hold back the 19-year-old De Minaur. "It's probably the hottest day we've had and very humid as well - long rallies and pretty taxing", de Minaur said after his triumph. I feel like I'm playing great tennis.
In competition though, de Minaur is constantly labelled as a young Hewitt himself.
The Italian earned his first break point of the set before capitalising on a De Minaur double-fault to lead 4-3.
Barty also insisted she'd enter this year's tournament better placed and as a better player than the one who was knocked out last year in the third round.
The 19-year-old proved his burgeoning reputation as a fighter is deserved and he never looked in danger of suffering a repeat of last year's disappointment as he became the first Australian to lift the title since Bernard Tomic in 2013.
'I knew coming in that if I wanted to come away with a trophy, I was going to have to play two really tough matches, ' he said.