Serena Williams, who gave birth to her first child last August, was playing in her first official WTA tournament since winning the 2017 Australian Open.
Venus was leading 5-2 when she wasted a match point and the 37-year-old needed to fend off a break point in the 10th game before closing it out. "For her, I think it was a really good match", Serena said.
Federer improved to 65-5 since returning from a left knee injury previous year with his third-round victory in a rare day match.
Serena was a mere shadow of her past self and managed to win just 54 percent of her first serve points in the first set.
Serena Williams said on Saturday she "literally didn't even think about" the canceled 2001 match. I don't want to go backwards'.
After 14 months away from professional tennis, Serena Williams, now a mother, is healthy and hitting hard, but not enough to beat her sister Venus. In the press conference after his win over Federico Delbonis, Federer has cleared that he will take rest, following his participation in Indian Wells and Miami.
But the lesson from Indian Wells this week is that the Williams story is nowhere near over yet. It was really hard to close out the match.
Retired mixed martial artist Chuck Liddell sat in the Champions Box near tournament owner Larry Ellison and top-ranked Simona Halep was also in attendance for the match.
According to BBC, more than 10,000 fans gathered into the arena to watch the Williams sisters. Venus did her usual pirouette, but still didn't release a smile.
And that's precisely what Venus did. She finished out the match cranking a mighty serve and riding an improved forehand that continually blasted shots with velocity from the baseline.
"I'm just lucky that I've played more matches than her right now", Venus said on court afterward. "That's all I see", Venus said. It's good that I don't have to say that this is the best tennis I have ever played and I lost. Venus won just four more points than Serena overall - we can use first names here, because chair umpire Juan Zhang made a decision to go that route.
Venus broke Serena's service four times in two sets which set up her win in the third round. Venus and Serena were set to face off at the semifinals that year until Venus withdrew, citing a knee injury, causing dissatisfaction from the crowd.
But neither of them spoke publicly about it while they were here, and instead chose to focus on Serena's return to the World Tour. I have such a long way to go. It's definitely not less disappointing. I'm still making errors that I don't normally make. "It's just afterward I don't like it as much". "I'm playing a completely different player, new challenges".
Venus doesn't anticipate that trial run being very long.
Serena concurred: "I haven't played in over a year..."