Barty, who will begin in the second round at Memorial Drive after a bye, takes on Russia's Anastasia Pavlyuchenkova, who defeated Estonian Anett Kontaveit 6-2, 6-4.
"It was very hard, but I like the heat and I'm happy to be here for the first time", said Bencic, who topped the rankings a year ago and won 49 on her way to one of the two titles in Moscow and Dubai best games of career.
"I have seen the physios, I have seen the doctors, and I will be continuing to do that for the whole of the week and hopefully I will be ready to play in Melbourne", he added. We've always had very close ones.
"I definitely was able to find a bit more of my kind of style of tennis and control the match a little bit more in the third", Barty said.
He was the second seed to pull out after Novak Djokovic, who led Serbia to the ATP Cup title in Sydney, opted to head straight to Melbourne ahead of his title defence at the year's opening Grand Slam.
"Credit to Anastasia; she hung around and got more aggressive in those latter games".
Nearly a year after he lost to Nadal at the Australian Open (winning just seven games in a three set loss) his game has come on immensely, he said.
"With everything going on around the country right now, all in all it makes me bloody proud to be an Aussie", she said.
"This is my first win of the year, I'm happy about that".
Barty will next play either Australian qualifier Arina Rodionova or Czech eighth seed Marketa Vondrousova in a Thursday quarter-final.
The American, whose last match was a second-round ouster in Beijing on October 1, exited in 72 minutes, dropping serve four times.
Rodionova worked her way through qualifying rounds, defeating a pair of top 100 opponents to earn her spot in the draw. "I crave it. I love it", she said. "I feel pretty good about myself right now".
Elsewhere, Maria Sakkari of Greece made quick work of Vitalia Diatchenko of Russian Federation 7-5, 6-2.
While she is expected to now relink with her regular doubles partner Coco Vanderweghe - with whom she won the 2018 US Open - she thanked Bertens for agreeing to partner her "in my lovely hometown of Brisbane" for the first tournament of the season.
In the men's draw Britain's Dan Evans, also fresh from the ATP Cup, beat Argentinian Juan Ignacio Londero 6-2, 6-4 while Jeremy Chardy overcame fellow Frenchman Gilles Simon 6-3, 7-5. American qualifier Tommy Paul beat Aljaz Bedene 6-4, 6-4.