The American improved to 105-52 her career win-loss record in WTA main draw tiebreaks and sealed an early break at 2-1 as the Dutch amassed a couple of forehand errors.
Neither woman played in the desert a year ago.
2018 Australian Open champion and second seed Caroline Wozniacki moved into the 3rd round at Indian Wells after defeating Lara Arruabarrena 6-4, 6-1.
Nick Kyrgios withdrew Friday, citing a lingering elbow injury. Verdasco will likely now face Grigor Dimitrov in the next round. He'll be replaced by lucky loser Matteo Berrettini.
Despite Serena Williams talent and wins, the 36-year-old tennis Titan has been ridiculed for what many deem inappropriate behavior for a woman.
Venus beat Romania's Sorana Cîrstea 6-3. 6-4.
"It truly means the world to me to just be able to be here, to play, to enjoy myself and do what I love to do", she said. This year, each time the sisters walk onto center court, an announcer greets them by saying, "Welcome home, Serena!" and "Welcome home, Venus!".
The sisters will resume their longtime rivalry on Monday.
In Serena's last tournament before maternity leave, she defeated Venus in the final of the 2017 Australian Open. She was unseeded in the tournament, and was squared up against world number 53 in her first match.
She'll be taking on sister Venus in the third round and talked about playing the opponent that she does not like playing: "She's had such a good year last year and playing fantastic tennis".
Williams said she nearly cried before her match because she missed her daughter, who was sleeping at their home while the rest of her family watched in the stands.
In the men's tournament at Indian Wells, Roger Federer's opening match was put on hold as heavy rain swept through the California desert.
The two-time Indian Wells champion featured at the recent Tie Break Tens event in NY and appeared in fine fettle as she entertained the crowd.
Their very first meeting was scheduled to be that semi-final in Indian Wells in 2001, making this their first ever contest here since putting together a tally of 30 Major singles titles, 14 Major doubles titles, and four Olympic golds.
Bellis led five Americans into the second round.
Two seeded players lost: No. 18 Magdalena Rybarikova and No. 28 Anett Kontaveit.
Carla Suarez Navarro (27) of Spain beat Taiwan's Su-Wei Hsieh 6-4, 2-6, 6-3 while Australia's Daria Gavrilova (26) dismissed Belgium's Yanina Wickmayer 7-6 (3), 6-2.
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