Alcaraz hit 31 winners in a comprehensive 6-4, 6-3 victory over Norrie at the Indian Wells Tennis Garden in California in the United States to advance to the last four for the first time.

The 18-year-old becomes the second-youngest men's singles semi-finalist in Indian Wells Masters history behind American Andre Agassi, who reached that stage at the age of 17 in 1988.

He is now set for an all-Spanish semi-final against 21-time Grand Slam singles champion Nadal who was forced to dig deep to see off Australia’s Nick Krygios 7-6, 5-7, 6-4 to extend his winning run at the start of the season to 19 matches.

"It's tough to play against Rafa but at the same time I will enjoy the moment, I will enjoy the match," said Alcaraz.

"It's not every day you play against your idol.

"I'm going to be happy even if I lose that match, but I am focused right now to play my best against Rafa and be able to take my chances."

Nadal came under threat against Kyrgios as he fell 4-2 behind before breaking back in the 10th game and then cruising through the tiebreak without dropping a point.

Kyrgios responded to take the second set as he attempted to claim a fourth win over Nadal.

But Nadal emerged victorious to improve his head-to-head record against the Australian to 6-3.

"It’s difficult to play against him, always tough because he changes the dynamic of the point very quick and his serve is huge, especially the first serve," said Nadal.

"Nick is one of these kind of players that you're going to have problems when he’s motivated."

Kyrgios let his frustration get the better of him during the quarter-final meeting and almost hit a ball boy at the end of the match.

After shaking Nadal’s hand at the net, Kyrgios hurled his racket to the floor before it bounced and came close to striking the ball boy at the back of the court.

"It was a complete accident," said Kyrgios.

"I didn't hit him, thankfully.

"It wasn't my intention so thankfully the ball kid's okay."

In the women’s singles, defending champion Paula Badosa of Spain progressed to the semi-finals with an impressive 6-3, 6-2 win over 21st seed Veronika Kudermetova.

Competing as a neutral, Russian Kudermetova had no answer to Badosa who extended her winning streak in Indian Wells to 10 matches.

The world number seven will next face Greek sixth seed face Maria Sakkari, who recovered from an early break in the first set to down Kazakhstan’s Elena Rybakina 7-5, 6-4.

"I think I had a rough start," said Sakkari.

"I was a little bit nervous.

"But then I just had faith in my game.

"I knew that if I could break her back, I would get back into the match.

"Making a lot of balls after being 4-1 down gave me a good chance to come back into the match."

Badosa and Sakkari will meet tomorrow while the other women’s singles semi-final sees Romania’s Simona Halep and Poland’s Iga Świątek go head-to-head.

The two remaining men’s singles quarter-finals will also be held tomorrow with Russian Audrey Rublev, competing as a neutral, taking on Bulgaria’s Grigor Dimitrov and Miomir Kecmanović of Serbia facing American Taylor Fritz.