The twenty-three time Grand Slam winner outclassed former French Open semifinalist Bertens, 7-6(5), 7-5 in just under two hours.
This is Serena's first tournament after the 2017 Australian Open victory, where she was pregnant.
"It definitely felt better than the first round, but I'm still a little rusty. I'm still making errors that I don't normally make. I call this a trial run, of traveling with the baby and all of this is just so new to me," Serena said post her win.
Meanwhile, Venus reached the round of 32 after defeating world No. 35 Sorana Cirstea 6-3, 6-4 in just 79 minutes.
The Williams sisters have faced each other 28 times in their legendary careers where Serena has a 17-11 head-to-head record over Venus.
She's had such a good year last year and playing fantastic tennis. But I have to play a seed regardless, sooner than later most times for the next couple of tournaments. So I have to be ready. Whether it's Venus or anyone else, it's going to be someone," Serena said of her clash with sister.
She added, "Obviously I wish it was anybody else in the draw, literally anybody, but that's okay. Just have to go out there and see how I am and do my best." (ANI)