The first set remained on serve until 2-3, when Cilic broke to move 4-2 ahead, before eventually claiming the set 6-3 at the second time of asking.
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The response from Chardy was strong, however, with the Frenchman securing back-to-back breaks at the end of the second to level the match at one set all after little over one hour of tennis.
Both players claimed the first two sets in fairly routine fashion, but a tie-break was left to decide the third after each held their serve for all twelve games. Cilic took control of the breaker in the first point and Chardy simply never recovered as the reigning US Open champion moved 2-1 ahead with a score of 7-2.
Cilic's dominance continued into the fourth set when he secured back-to-back breaks, in addition to two holds, to move 4-0 ahead. A third hold moved Cilic to within one game of victory, but Chardy did manage to hold for 5-1.
The 26-year-old Croatian was not to be denied, however, as he served the match out in routine fashion to make the quarter-finals once again. As for Chardy, a fourth-round spot this year represents his best-ever showing at the US Open.