Pera, who benefited from Briton Johanna Konta's withdrawal, started on the front foot by breaking her Dutch opponent in the opening game.
The 24-year-old more than held her own and earned an opportunity to close out the first set at 5-4, before Bertens switched gears to draw level.
Kvitova overcomes Barty to take Sydney International title
Another break in the 12th game saw Bertens clinch the opening set.
Bertens let two match points go at 5-4 in the second but she would not be denied as Pera served a double fault to concede the match after an hour and 45 minutes.
Seventh seed Bertens, who has never progressed beyond third round in six Australian Open appearances, will look to step up her preparations for next week's Grand Slam at Melbourne Park with a second round meeting with Garbine Muguruza.
Two-time Grand Slam winner Muguruza eased past fellow Spaniard Carla Suarez Navarro 6-3 6-4.
In the men's draw, local favourite Alex de Minaur, who reached his first Tour final in Sydney last year, made a winning return to Ken Rosewall Arena, beating Serbia's Dusan Lajovic 6-4 6-3.
The Australian number one said it would be a dream to lift his first career title this week in his hometown.
"Honestly it would be like a dream come true, but we are still far away from that," he said.
De Minaur will meet American qualifier Reilly Opelka for a place in the quarter-finals.
Opelka powered past Spain's Albert Ramos-Vinolas 6-3 6-4, firing 16 aces and dropping just eight points on serve.
Halep stunned by Barty in Sydney second round
Kerber swats aside Giorgi to reach Sydney quarter-finals