The Spanish defending champion had a score to settle with the 58th-ranked Hungarian after losing their only other meeting at last year's Rome Masters.
Alcaraz never let his opponent into the fourth-round match, breaking twice in the opening set and winning 12 of the first 13 points of the second.
The top seed reeled off 22 winners in 75 minutes to race into quarter-finals.
After a slow start this season and an ankle roll several weeks ago in Brazil, Alcaraz appeared on course to continue his chase to a possible second title here.
"I was nervous before the match, I'm not going to lie," the winner said. "I was playing someone who beat me when I had no chances in the Rome match.
"It was difficult, but I'm happy with how I did. I knew what I had to do - something I did not do last time.
"I played great in the first set and kept pushing in the second. I wanted to break as soon as possible and go up in the score."
The world number two marked his 50th Masters victory with the defeat of Marozsan, and his ninth straight win in Indian Wells.
Alcaraz is on course for a possible collision with Australian Open champion Jannik Sinner in the semi-finals but will first need to get past Alexander Zverev.
The big-serving German sixth seed wore down Australian Alex de Minaur with his relentless power to claim a 5-7, 6-2, 6-3 victory.
Sinner shaded a tight first set against American Ben Shelton in windy conditions and met with little resistance in the second, securing a 7-6(4), 6-1 win to maintain his perfect record in 2024.
"I just tried to stay positive," Sinner said.
"There were tough moments, especially in the first set, and I'm really happy that I won that and started really positive in the second set, which gave me a lot of confidence."
Third seed Sinner will be the favourite when he faces Jiri Lehecka for the first time in the quarters.
Lehecka, seeded 32nd, backed up his upset of fifth seed Andrey Rublev with another over 11th seed Stefanos Tsitsipas in a dominant 6-2, 6-4 win to reach his first ever quarter-final at a Masters 1000 event.
The 22-year-old Czech piled up 25 winners against the Greek player and has not dropped serve in his last two matches.
