Two-time defending champion Alcaraz overcame a 4-1 second-set deficit to defeat Francisco Cerundolo 6-3 7-6 (7-4) and will play Jack Draper in the semi-finals after the Briton dispatched Ben Shelton 6-4 7-5 in a battle of lefties.
Shelton, at 22 the youngest American man to reach the quarters at Indian Wells since 2004, couldn't go further.Â
The 13th-seeded Draper will face No.2 seed Alcaraz, who extended his winning streak at the ATP 1000 event to 16 matches with victory over Argentine Cerundolo.
Alcaraz, who has said Indian Wells is his favourite tournament outside of Spain, wondered if he should make his home away from home official after winning his 16th consecutive match in the desert.
"Should I buy a house here?" he wrote on the TV camera lens after his victory.
"Today was about surviving, I'm proud of everything I've done today," Alcaraz said after improving to 2-0 in his head-to-head series against Cerundolo.
"Tennis is about getting the win. It doesn't matter how you do it. You're not thinking about playing great tennis every match, every day ... It's about good behaviour, mental strength, just to stay there all the time, trying to get a good rhythm. I didn't hit the ball as clear as yesterday, for example, but I just did what I had to, and that's what tennis is about."
Earlier on Thursday, Daniil Medvedev jumped for joy in an uncharacteristically emotional celebration after holding off Frenchman Arthur Fils 6-4 2-6 7-6 (9-7) amid gusting winds on centre court.
The Russian took advantage of 19 unforced errors from Fils in the first set but the 20-year-old showed maturity beyond his years in the second, using backhand slices and making frequent trips to the net to level the match.
Momentum swings were frequent in the deciding set and tiebreak, and Fils smashed his racket after sending a volley long facing match point.
"The adrenaline got me going," Medvedev told reporters.
"I jumped next to him. Then I was, like, sorry man, I usually don't celebrate like this, but it's OK, it can happen."
Next up for the fifth seed is Dane Holger Rune, who beat Dutchman Tallon Griekspoor 5-7 6-0 6-3.
With AP.
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