In an entertaining baseline duel at the Margaret Court Arena, sixth seed Cilic blew away Carreno Busta in the tiebreaks to celebrate his 100th grand slam win.
A former semi-finalist at Melbourne Park, Cilic also equalled Goran Ivanisevic's Croatian record of 11 grand slam quarter-final appearances.
Carreno Busta showed heart to rally from a break down in the fourth set and push the match into a third tiebreak but was quickly overwhelmed by Cilic's firepower as the Croatian brought up four match points in a hurry.
Cilic blew one of them by spraying a crosscourt shot wide but made no mistake on the second, hammering a huge first serve down the 'T' and picking off the return with a straightforward forehand winner, bringing raucous cheers from the large Croatian contingent in the terraces.
The 2014 U.S. Open champion Cilic will meet either last year's finalist Rafa Nadal or Argentine Diego Schwartzman for a place in the semi-finals.
"It was an unbelievable match, a lot of ups and downs," Cilic said in his on-court interview.
"Pablo came back and really gave me a lot of trouble ... We had a lot of tough rallies so I was really glad how I stayed in there mentally."
(Editing by Sudipto Ganguly)
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