The day first saw the second seed Simona Halep defeat Kateryna Kozlova 7-6, 7-5 while Serena Williams lost the opening set before retiring from her match against Garbine Muguruza with a viral illness.
Williams had gone 3-0 ahead but after losing six consecutive games, she called for the trainer.
Barty, the Australian 12th seed, was in fine form as she brushed past wildcard Jennifer Brady 6-3 6-2, setting up a meeting with Svitolina.
During the interview at the end of the match, Muguruza wished Serena a quick recovery; "I wish I am going to see her very soon and better!"
Former Wimbledon and French Open champion Muguruza was happy with the way she had been playing against Williams before the American's retirement.
Then Williams faced, in her first seed, multiple Major champion and former No1 Garbine Muguruza, ranked here at 20 after a dip in her results in the a year ago or so.
Browns acquiring OBJ from Giants
Cleveland, meanwhile, makes another big move as it looks to reach the playoffs for the first time since 2002. The Browns will trade a first round pick, third round pick and Jabrill Peppers to the Giants for Beckham.
"We've played many times and it is always super tough and super exciting".
Serving for the match, Bertens saved one break point and let two match points slide by before she reached the round of 16 for the first time at Indian Wells when Konta sent a forehand wide.
Muguruza hopes for more good feelings in her next match, a fourth-rounder against Kiki Bertens of the Netherlands.
The Romanian finally put away the 114th ranked Kozlova with eight consecutive points in the second set, a backhand victor proving the decider just as it had in the first set. The Swiss ace won the first set 6-1 but had a more hard second set, which ended 7-5 while Nadal surrendered just two games against this American opponent winning 6-1,6-1.
Serena Williams (R- sitting) withdrew midway through her match against Garbine Muguruza. In all, he owns five titles at Indian Wells. I think his serve really picked up.
"It is different from past year, but I think I am getting used to it, " Osaka said.