The 20-year-old world No.204, who also has a wildcard at the upcoming Australian Open, finished with a flurry to beat the Slovakian No.72 6-4 6-1 on Wednesday.
She dropped the opening game of the second set in the second-round match before reeling off six straight.
"I think I handled myself really well in that situation. I just tried to stay relaxed and trust what I was doing," Preston said.
"It's something that me and my coach have talked about, just playing fearless.
"With the way I play, I'm probably going to miss a few shots but just keep going for it and commit and trust what I'm doing."
Preston, who hails from Western Australia, pulled off the biggest win of her career rankings-wise in the opening round, accounting for fifth-seed Jessica Bouzas Maneiro.
She hit a career-high ranking of 134 in 2024 but fell outside the top 200 heading into this season.
"I've had a bit of a tough last 12 months," she said.
"So to be able to get my confidence up and know that I can compete and win at this level is a massive booster and hopefully sets myself up for the rest of the year."
Preston will meet grand slam champion and top seed Emma Raducanu in Thursday's quarter-finals.
Raducanu was gifted passage into the final eight after Polish world No.72 Magdalena Frech withdrew from their second round encounter with a left thigh injury.
"It would be a really cool experience for me to test myself (against Raducanu)," Preston said before Frech's withdrawal.
"She's won a grand slam and is obviously a very, very good player."
At last year's Hobart, Australia's top-ranked woman Maya Joint sparked a breakout season with a run to the semi-finals from outside the top 100.
Raducanu, who won the 2021 US Open as a qualifier, got through to the second round on Wednesday when she finished off a rain delayed match against Maria Camila Osorio Serrano.
The Brit came from behind in the second set for a 6-3 7-6 (7-2) victory - her first of 2026.
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