Just one day on from his 19th birthday, Alcaraz - who many expect to replace Nadal as the undisputed King of Spanish tennis - overcame an ankle injury to defeat the 35-year-old 6-2 1-6 6-3.
The teenager suffered the injury in the second set and seemed like he might not continue after going over on his right ankle.
Nadal went on to reel off five straight games to win the set and level the match. However, Alcaraz began to move freely in the decider and held on to an early break of serve to complete a historic first victory over his idol.
The Spaniard became the first teenager in history to beat Nadal on clay. Speaking afterwards, Alcaraz said: "I'm very excited, a lot of excitement. Very few players can say that they have defeated Rafa on clay. I feel fortunate to be one of them."
The youngster lost his previous two meetings with Nadal, but with the 21-grand slam winner entering the match on the back of a marathon clash against David Goffin, Alcaraz was able to take full advantage.
When asked whether this result represented a changing-of-the-guard moment, Nadal said: "Of course it's a handover. If it's today or not, we will see the next months. I'm happy in that regard. He has been better than me in several aspects of the match and several aspects of the game, and I need to improve."
Nadal had just recovered from a stress fracture of a rib, but the Spaniard will head to Rome for the Italian Open as he continues his preparations for the forthcoming French Open.
Nadal added: "My only dream is to be in Paris healthy enough and physically good enough to compete at the highest level possible. If that happens, I know it's a tournament that I have been playing well a lot of times in my career. Why not I can be competitive again and give me one more chance."
Alcaraz, in contrast, will now set his sights on world number one Novak Djokovic in the Madrid Open semi-final. The Serb put on a high-quality display as he dispatched Poland's Hubert Hurkacz in straight sets, winning 6-3 6-4.
Speaking after the win, Djokovic said: "I was serving really well in the second set, I think that kept me alive.
"I was pleased with the way I was constructing points. I tried to make him run and miss and overall it was a solid performance.
"It's definitely a positive indication that I am on the right track in terms of getting to the desired level of tennis, being in one of the best tournaments in the world where all the best players are playing. Of course it does give me confidence, and it encourages me to keep going."