The 36-year-old Swiss superstar can equal his season-best start of 16-0 with a win in the quarterfinals, where he will meet Chung Hyeon of South Korea in a rematch of their Australian Open semifinal.
"This might be the last day, so we'll see," Federer said, smiling. "Don't jinx it."
He advanced to the final in Melbourne when Chung retired in the second set trailing 6-1, 5-2 because of blisters on his left foot. Federer went on to win a five-set final against Marin Cilic for his 20th Grand Slam title.
Chung, seeded 23rd at Indian Wells, beat 30th-seeded Pablo Cuevas of Uruguay 6-1, 6-3.
Since his Grand Slam breakthrough Down Under, Chung has been on a roll. He's reached the quarterfinals or better in four of five tournaments and improved to 15-5 this year.
"I was honestly quite surprised how quickly he came back," Federer said. "Because that thing looked nasty and it takes some time to heal. But he seems fine and he played a great match today. So I'm excited to play against him."
Federer is chasing a record sixth title in the desert.
"Just playing really fast and good serve, good baseline," Chung said of Federer. "He play everything good, so I'm just trying to enjoy on the court."
Against Federer, Chardy played a tough first set in windy conditions that persisted throughout the day. Federer earned the only break in the 11th game and then served a love game to take the set.
Federer again took the only break in the second set to go up 5-4. His forehand pulled Chardy completely off the court and Federer hit a crosscourt backhand winner off Chardy's return. Federer served his fifth love game of the match to close it out.
Chardy committed 46 unforced errors to 29 for Federer, who won 90 percent of his total service points.
Against Cuevas, Chung dominated in racing to a 6-1, 5-0 lead before Cuevas fought off seven match points to break back in the sixth game. Cuevas then broke Chung again to close to 5-3, but the Korean closed out the win.
"It was a really tough match against Pablo," Chung said. "I have few match points but start (getting) windy and he playing good. Not easy to play with the wind, but I'm just trying to focus all the time."
Simona Halep also fought the wind and a pesky opponent to reach the semifinals, where she will play Naomi Osaka of Japan.
Osaka knocked off No. 5 Karolina Pliskova of the Czech Republic 6-2, 6-3.
Halep, ranked No. 1, outlasted Petra Martic of Croatia 6-4, 6-7 (7), 6-3 and improved to 18-1 in matches this year.
Winds gusting to 15 mph made shots tricky. Trailing 4-2 in the first set, Martic closed to 5-4 before Halep served it out.
"I was a little bit frustrated about the game today because the wind didn't give us the rhythm," Halep said in an on-court interview. "That's maybe why I'm here because I refuse to lose."
Martic controlled the second set, taking a 5-2 lead before Halep forced the tiebreaker. The Romanian tied it 5-all before Martic won the final two points to force a third set. Halep rallied from a 2-1 deficit to tie it 3-all before winning the last three games.
"I calmed down myself a little bit more," Halep said. "I just was more focused on what I have to do, not thinking that much about the wind and what is going on on court."
In other fourth-round men's matches, No. 6 Juan Martin del Potro beat fellow Argentine Leonardo Mayer 3-6, 7-6 (7), 6-3; No. 18 Sam Querrey defeated No. 28 Feliciano Lopez of Spain 6-3, 6-4; Borna Coric of Croatia outlasted American Taylor Fritz 6-2, 6-7 (8), 6-4; and No. 31 Phillipp Kohlschreiber of Germany beat Pierre-Hughes Herbert of France 6-4, 7-6 (7).
Del Potro will face Kohlschreiber in the quarterfinals. Coric next plays No. 7 Kevin Anderson of South Africa, who beat No. 11 Pablo Carreno Busta of Spain 4-6, 6-3, 7-6 (8).
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