In her first game back since giving birth, Williams defeated Diyas 7-5, 6-3 in the first round.
Serena then took centre stage, needing just under two hours to dispatch Bertens, of the Netherlands, 7-6 (7/5), 7-5. "Everything is a bonus". Monday's match will be the 29th between the pair, with Serena leading the head-to-head record 17-11. "You know it takes time to get back".
The Guardian reports that Williams received a standing ovation from her family after winning the match.
Williams is healthy again, but skipped this year's Australian Open because she did not consider herself tournament ready.
They went on to a tiebreak in the first set. "I'm just out here on this journey doing the best I can".
Williams, with husband and Reddit co-founder Alexis Ohanian looking on, was only two points from dropping the opening set but showed the sort of poise that earned her 23 Grand Slam singles titles.
"It's official. My comeback is here", she said.
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Venus is making her seventh appearance in Indian Wells and is the oldest player in the women's draw. "This whole month I am playing tournaments in California and Florida- both my home states", she wrote. "We always have a couple tight sets". It's such an unbelievable feeling to be back playing and having fun - I forgot what it's like playing in different emotions. "So it's definitely a lot easier to play later on".
The first set could have gone either way as Bertens troubled Williams, though the Dutchman's serve proved to be her downfall. "Now that she is not dominating, women's tennis is more interesting".
Bertens won just 55 percent of her service points, and Williams managed to convert five of her nine break-point opportunities.
The second set was less straightforward with five successive breaks of serve as each time Williams thought she had the advantage, the Khazak peged her pack.
But all-Williams matches have never been exclusively about the tennis or the tactics. I went in there knowing I'm not going to be my best these first few matches, but I'm playing with nothing to lose.