Two-time major winner Alcaraz said he was “nervous” before his meeting with Marozsan, having lost to the world number 58 in straight sets at last year’s Italian Open.
“I was nervous before, I’m not going to lie. Playing against someone who beat you easily, I remembered I had no chances to win the game in Rome so it was difficult for me,” Alcaraz said.
“Today I knew what I had to do better than I did in Rome.”
Alcaraz broke twice in the opening set and claimed the decisive break in the sixth game of the second to seal his place in the last eight for a third consecutive year at Indian Wells.
The 20-year-old added: “I did a few mistakes that I didn’t want to make so that’s what I want to be better. I want to serve better. It doesn’t mean today I served bad but I want to keep improving and putting good tennis on the court.”
In the women’s draw, 16th seed Elina Svitolina lost 6-1 4-6 6-3 to American Emma Navarro, while her Ukrainian compatriot Marta Kostyuk reached the last eight with a 6-4 6-1 over Russia’s Anastasia Pavlyuchenkova.
Kostyuk will face Russia’s Anastasia Potapova, who beat Italian 13th seed Jasmine Paolini 7-5 0-6 6-3.