Gauff won 6-3, 6-2 on Rod Laver Arena to set up a last-16 clash against 2017 French Open champion Jelena Ostapenko.
A maiden Grand Slam title for seventh seed Gauff would make her the youngest Melbourne champion since a 16-year-old Martina Hingis 26 years ago.
Gauff headed into the first major of the year on a high after winning her third WTA title at the Auckland Classic earlier this month.
She admitted she "got lucky" in her tight second-round victory over Emma Raducanu in a battle of tennis prodigies.
But Gauff let her racquet do the talking in her first meeting with power-hitter Pera, relentlessly soaking up some late pressure from the world number 41 when serving for the match at 5-2.
"She was hitting the ball really hard," said Gauff, who this week became the first woman to register 100 tour-level wins before her 19th birthday since Caroline Wozniacki in 2009.
"So I was trying to hang in there and take the ground when I could.
"Last season she had a really long match streak so I knew she would be a tough player to beat, so I'm glad to be through to the second week."
Gauff is one of two teenagers left in the women's draw. The other is 17-year-old Linda Fruhvirtova, who plays Marketa Vondrousova in an all-Czech third-round clash on Saturday.
AMERICANS PUSHING EACH OTHER
Gauff said the camaraderie and desire among American players to improve collectively is the driving force behind their impressive showing at this year's Australian Open.
U.S. players appear to have carried their form from their victory in the inaugural United Cup mixed team tournament earlier this month into the Melbourne Park Grand Slam.
Gauff is among a number of American women to have made it to the third round, but Danielle Collins and Madison Keys were eliminated.
The country's hopes have also been rekindled in the men's singles draw, with eight players in the third round, though Mackenzie McDonald lost to Yoshihito Nishioka and Frances Tiafoe was eliminated by Karen Khachanov.
No male U.S. player has captured a Grand Slam title since Andy Roddick at the 2003 U.S. Open.
"I definitely think on the men's side they're thriving really. It's like eight people in the round of 32 I saw. I think it's incredible," Gauff told reporters on Friday.
"That would be pretty cool if an American woman and guy could win the same slam. I definitely think the guys are feeling it. I think it really comes from, not the women, but the same dynamic, where everybody is doing well, so it makes you want to do well.
"We're all not competing with each other, but pushing each other. I think that's what the men are having... I'm pretty sure all the American guys get along, at least that's what I think."
Gauff added that the men's and women's players had forged a strong relationship that extended beyond tennis.
"I always look forward to the joint events," Gauff said.
"When they're playing, I look at the draw and I'm happy they're in the draw. We went mini golfing the other night. It's something I want to do more at more tournaments especially."
