The Spanish teenager is yet to drop a set in Cincinnati.
Alcaraz had a chance to serve out the opening set at 5-4, but Cilic rallied to break back and eventually force a tiebreaker.
The 19-year-old sensation raced to a 5-1 lead and never looked back, taking the momentum into the second set which he wrapped up in 34 minutes.
Granted, Cilic made a plethora of unforced errors (27) but it was another impressive display from the rising star, who has already scooped five ATP Tour titles since turning professional last year.
"I know that Marin is a really aggressive player," the world number three told the press after his victory, as per atptour.com.
"I had to be really focused on the match. I knew that it was going to be a tough match, that I had to be [mentally] in the match all the time. I knew that I was going to have my chances to break his big serve.
"So I'm really happy with the performance and the focus in the match."
Next in line for Alcaraz is ninth seed Norrie. The British hopeful made short work of Ben Shelton, needing just 59 minutes to win 6-0, 6-2 and book his place in the quarter-finals.
Elsewhere, seventh seed Filipe Auger-Aliassime came back from a set down to defeat 10th seed Jannick Sinner of Italy 2-6, 7-6, 6-1.
The young Canadian faces Borna Coric - who knocked out Rafael Nadal earlier in the tournament - in his last eight clash on Saturday.