"It was a very interesting match", Williams said afterwards.
Williams came back in style against world number 29 Bertens, winning 5-7 6-3 7-5.
She had four break points to take a 3-0 lead two games later, only for Williams to power down first serves approaching 120 miles per hour to save herself.
"The first set was definitely all her, and she came up with some incredible shots to break me at 5-5.There was not much I could do there, except just hope I could keep up in the second and third sets", the WTA quoted Venus, as saying.
"I'm not sure", the eighth seed said on court when asked how she had pulled off the victory in a match that had 15 breaks of serve.
Konta, whose victory here a year ago propelled her into the top 10 in the world rankings, advanced with relative ease, beating Belgian Elise Mertens 6-2, 6-1.
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Though Konta beat the eighth seed on her way to the title in Florida previous year, she had since lost to Williams in Rome and Wimbledon as part of a tight 3-3 head-to-head. "It didn't look good sometimes but that's why you keep playing to the last point, and why I love this game".
Konta has endured a poor 2018, but back-to-back straight-sets victories has lifted the Brit this week.
Fourth-seeded Elina Svitolina and sixth-seeded Jelena Ostapenko, the reigning French Open champion, also advanced, as did 2016 Olympic gold medallist Monica Puig.
At the end of the set the fading British number one called for the physio and took a medical timeout in order to have treatment on her lower back. The American, pursuing her fourth title here, came back from a break down in both sets to defeat qualifier Vikhlyantseva in her debut match on Friday.
Once again, the 37-year-old found her composure at the start of the second, breaking for a 2-0 lead.
Kerber was made to sweat in her gruelling clash with China's Wang Yafan before prevailing 6-7 (1-7) 7-6 (7-5) 6-3.
Williams faced more breakpoints in the third although this time the danger was averted, thanks to some powerful serves.