"I think it's such a treat for everyone to see this match so early in her comeback", Venus said.
"These courts are really hard to play on". Not all of the time, but most of the time.
"I haven't played in over a year", Serena said in quotes on the WTA's official website. "So I'm very happy how things are turning out to be".
Venus faced two break points in the next game, but got bailed out on Serena's consecutive forehand errors to get to deuce.
Her stamina appeared to get better as the match progressed, and she won several long points. The other victory came in Rotterdam.
Venus will now be up against 21st seeded Anastasija Sevastova of Latvia in the fourth round of the tournament.
Also, American Taylor Fritz defeated Fernando Verdasco of Spain, 4-6, 6-2, 7-6 (7/1), Croatia's Borna Coric breezed past Roberto Bautista 6-1, 6-3 and Pablo Carreno-Busta of Spain, stopped Russian Daniil Medvedev 6-1, 7-5.
Venus raced out to leads of 3-0 and 5-2 in the second set.
To say Williams is back would be a rush to judgment for the 23-time Grand Slam singles champion, who was playing her first competitive singles match since winning the 2017 Australian Open title last January.
"I definitely know her well", Serena said of her sister.More news: Apple buys 'Texture' Magazine Subscription App
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Wozniacki said the court conditions were hard but she managed to make the adjustments.
"It was good to play and try to get in the rhythm and get into the swing again", added Serena, who gave birth just over six months ago. I think this will change a little bit in the future, but for sure the game is good and not really any weakness. She lamented missing shots she said she would make 10 times out of 10 in practice.
Venus, who historically hasn't been able to consistently beat her younger sister, was in better physical condition in this matchup and advanced with the 6-3, 6-4 win.
The sisters arrived outside the stadium together on a golf cart then walked through the tunnel with Serena entering the court first with many in the crowd standing and cheering. Serena then held to force Venus, now with eight double faults, to serve for the match. I just want to continue to go forward.
Despite the loss Serena still leads their career series 17-12.
"It was not an easy match to figure out", Venus said of her victory Tuesday.
For a moment, the best women's player in the history of tennis displayed rare vulnerability.
But for some it brought closure to the once testy relationship between Indian Wells and the sisters who hail from the Los Angeles suburb of Compton. Now arguably the greatest sibling act in tennis history, Serena, 36, took the court as a new mother while Venus, 37, a new aunt.
Asked about the incident finally being put to rest, Venus said, "It never crossed my mind". She looked like Serena most of the time. "I thought I was in control of the point and winning the point, and she turned it around".
This is the earliest the pair will meet in a tournament since their 2nd round match in the 1998 Australian Open.