Serena won 7-6 7-5 against Kiki Bertens before Venus won 6-3 6-4 against Sorana Cirstea to tee up a third-round clash. "So it is what it is".
In other matches, another Argentinian Nicolas Kicker topped Jiri Vesely 7-5 and 6-3, and Federico Delbonis won against local boy Ryan Harrison 6-2, 4-6 and 7-5.
She joined American upset winners Sachia Vickery, who beat No. 3 seed Garbine Muguruza; 16-year-old wild card Amanda Anisimova, who beat No. 23 seed Anastasia Pavlyuchenkova; and wild-card teenager Caroline Dolehide, a three-set victor over No. 30 Dominika Cibulkova on Friday.
Asked about her preparation in playing her sibling, Venus said, "Really just trying to see what happens".
Williams was playing in her first Women's Tennis Association (WTA) Tour match for almost 14 months following the birth of her first child.
The Australian toughed it out in a first set tiebreaker before easing to a 7-6 (7-3) 6-2 victory.
Serena, who is returning to the sport after taking more than a year away to have a baby, was ragged at times but used her power to wear down the Dutch 29th seed in Indian Wells, California.
Talking to the audience and press after the game, Williams shared her thoughts over her impressive win against Diyas.
"As much as I like to tell you "it doesn't matter how I play here" I didn't come here to lose first round", he said.
But this year, with Serena now 36 and Venus now 37, they are finally set to play in the California desert.
Serena boycotted the event until 2015.
The Belarusian was making her first appearance since Wimbledon 2017. Williams broke her opponent five times in the 92-minute match.
Her husband and Reddit co-founder Alexis Ohanian looked on from the stands, as did her mother Oracene, sisters Lyndrea and Isha, her agent, and her coach Patrick Mouratoglou. First of all, 17 years ago seems like forever ago.
"I still have a lot to give".
I went in knowing I'm not going to be where I want to be in the first few matches.
She served a love game capped by a 100 miles per hour ace in her first service game.
Second seed Caroline Wozniacki had an easy time with qualifer Lara Arruabarrena 6-4, 6-1.
The 23-year-old Svitolina advances to the third round where she will face Spaniard Carla Suarez Navarro who beat Hsieh Su-Wei, of Taiwan, 6-4, 2-6, 6-3.