This was Cilic's 100th Grand Slam career win, securing him a place in the quarterfinals of a major for the 11th time, reports Efe.
"This is a beautiful (landmark) and I hope I can gather three more here," Cilic said after the match that lasted nearly three hours and half.
Earning his 100th Grand Slam win was not easy, as Carreno Busta rallied back from 2-5 down, pushing the set to a tie break, which the Spaniard won.
Cilic, the six-seed, was able to draw level thanks to two breaks in the second set, while he held his serve.
Both players managed to break the other's twice; Carreno Busta had a chance to serve for the third set with the scores at 6-5, but Cilic held firm.
During the third set tie break, Cilic routed Carreno Busta, who seemed like he could not get past the missed opportunity.
Cilic's momentum continued in the fourth set as he broke his rival's opening serve to love, only to be broken back in the sixth game.
The 2014 US Open champion Cilic held his serve during the rest of the set, as did Carreno Busta, with the former prevailing in the third tiebreak to advance into the last 8, where he will face Spaniard Rafael Nadal.
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