The two-time defending champion cruised past Thiago Seyboth Wild in the third round on Sunday to earn another comfortable win.
Alcaraz won 6-3 6-3 for his second straight victory in his first tournament since skipping Monte Carlo and Barcelona because of an arm injury.
"I think I played at a really good level," Alcaraz said.
"Coming into this match I was nervous a little bit because I didn't know how my forearm was going to be.
"Thiago has big shots. He is really strong. I am really happy with the performance. It was difficult a little bit at the end, at 5-0 and then serving at 5-3. I am really happy to get it at the end."
The second-seeded Alcaraz had made his debut at the tournament with a 6-2 6-1 win over Alexander Shevchenko.
Alcaraz had been scheduled to play at the Monte Carlo Masters and also missed Barcelona to try to fully recover ahead of the French Open next month.
"I think I'm in a good shape right now. I'm not feeling anything in the forearm, and I played good tennis," the 20-year-old said.
"Obviously I'm not hitting my forehand on my hundred per cent ... but I'm just focused to hitting the forehand as relaxed as I can. I'm really happy to be competitive without pain."
World No.3 Alcaraz is trying to become the first player to win three straight Madrid Open titles. He will next face Jan-Lennard Struff, his opponent in last year's final in Madrid.
Andrey Rublev continued his return to form with a 7-6 (12-10) 6-4 win against Alejandro Davidovich Fokina. The Russian had arrived in Madrid coming off a four-match losing streak before defeating Facundo Bagnis in his opening match.
Tallon Griekspoor got his first top-20 win on clay by defeating world No.12 Holger Rune 6-4 4-6 6-3 to reach the fourth round at an ATP 1000 event for just the second time.
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