The 22-year-old, who progressed from the qualifying rounds, won 1-6 6-3 6-4.

Dart will play Latvian eighth seed Anastasija Sevastova or Australia's Daria Gavrilova next.

"I'm really pleased to get the win. Priscilla played really good and it took me a while to get out of the blocks," Dart said.

"Everyone is fighting for every point so I had to keep doing what I was doing."

Dart started the year ranked 307th in the world but will end it in 149th, having won ITF titles in Altenkirchen and Oslo.

She made her Grand Slam debut at Wimbledon in 2018, losing in three sets to former world number one Karolina Pliskova in the first round.

Dart beat German former world top-10 player Andrea Petkovic and Kateryna Kozlova of Ukraine in qualifying in Brisbane.

Elsewhere, Czech Pliskova came from a set and a break down to defeat Yulia Putintseva, while world number 10 Daria Kasatkina fell to a shock defeat by Australian wildcard Kimberly Birrell.

Dutch sixth seed Kiki Bertens beat Belgium's Elise Mertens to set up a second-round meeting with Croatia's Donna Vekic, who overcame Magdalena Rybarikova of Slovakia.

In the men's singles, former champions Milos Raonic and Grigor Dimitrov are into the second round after defeating Aljaz Bedene and Yoshihito Nishioka respectively.