A sequence of seven straight games sent Bertens on her way to a 6-1, 6-2 victory, setting up a meeting with Galina Voskoboeva.
Bertens began the year on a losing note, succumbing to eventual champion Lauren Davis in the opening round at Auckland. Against Beck, however, she was soon into her stride overcoming an early break of serve to take charge of the contest.
"I'm really happy with this win, my first singles win of the year, and I'm really happy with my performance today," Bertens said. "I think I was playing OK in Auckland, but today was a really nice win and I think a really good start.
"In the beginning I was a little bit nervous because I really wanted this win and I think it's good to have some singles matches before going to Melbourne. But after a few games I started to feel the ball good, play some rallies and start to play more aggressive from there. That was the gameplan for today and I think I did that really well, especially the second set when I was moving really good."
A quarterfinalist 12 months ago, Bertens is the No.1 seed this time around and realizes this brings added expectation: "Of course there's a little bit more pressure - it's the first time I'm No.1-seeded - but I don't try to see it this way. I think everyone cane play really well here, so I think every match is a tough one so you have to be ready for every game."
Petkovic made short work of lucky loser Nicole Gibbs, while Lucie Safarova defeated Viktorija Golubic, 6-3, 6-4. Fett ended the hopes of former Roland Garros champion Francesca Schiavone, 6-3, 6-2, who afterwards confirmed that this year would be her last on tour.
"This is my last year of tennis. That's why I'm upset I didn't give the best showing here," Schiavone said. "This year I want to give everything that I've learned in the last 19 years.
"In life I think I've arrived at the time to take the decision," she said of her retirement, despite still feeling a passion for tennis. This sport is a drug for me, I love to play this sport."