Alcaraz took the opening set, but 21-time Grand Slam men's singles champion Nadal hit back in the second, sending the all-Spanish affair to a decider.

The teenager earned the only break of the third set and saw out a landmark 6-2, 1-6, 6-3 victory.

Nadal had won both of the pair's previous meetings, including on the Caja Mágica clay in this tournament in 2021.

"He's playing great, and I hope the best for him for the rest of the tournament," Nadal said of his opponent, with some viewing the match as something of a passing of the torch in Spanish men's tennis.

Next up for Alcaraz is Novak Djokovic, the world number one.

Serbia's Djokovic beat Polish player Hubert Hurkacz 6-3, 6-4 without facing a break point.

Greek fourth seed Stefanos Tsitsipas booked his spot in the semi-finals with a 6-3, 2-6, 6-4 win over Andrey Rublev.

Tsitsipas only won one more game than Rublev, who is Russian and allowed to compete as a neutral by the Association of Tennis Professionals, but made his two breaks of serve count.

Tsitsipas will face either Olympic champion Alexander Zverev of Germany in the final four, after he beat Canadian Felix Auger-Aliassime in straight sets.

The men's singles semi-finals are due to be played tomorrow, along with the women's singles final.