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Barty could face former champion Garbine Muguruza in the third round and awaiting in the quarterfinals could be defending champion Angelique Kerber or seven-time winner Serena Williams with twice champion Petra Kvitova a potential obstacle in the semifinal.
Federer, bidding for his 101st career title and a record sixth Indian Wells crown, received a walkover into the final, where he will play Dominic Thiem.
For a place in the semifinals, Serena Williams will meet Czech seventh seed Karolina Pliskova.
The Czech seventh seed broke former Wimbledon champion Muguruza five times in the one-sided clash at Margaret Court Arena.
The duo will take on Roger Federer and Belinda Bencic on Saturday in a repeat of last year's final.
Williams, who won the Wimbledon title on her last two visits in 2015 and 2016, is now on an 18-match winning streak at the All England Club.
It was not just the serve that caused mayhem for Muguruza. She slipped and fell heavily on her shoulder while chasing down a drop shot in the final set.
Marin Cilic, the 2017 runner-up, suffered a shock 3-6, 1-6, 6-4, 7-6(3), 7-5 defeat by Argentine Guido Pella.
Two-time former champion Petra Kvitova slumped out of Wimbledon in the first round, beaten by inspired world No. 50 Aliaksandra Sasnovich.