The defending champion powered down 19 aces on his way to a 6-2 6-3 7-5 triumph over the Russian on Arthur Ashe Stadium.
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The ninth seed suffered an early scare in the opening game, but he managed to save three break points before eventually snatching serve himself.
After edging ahead, Cilic found his stride to take a one-set lead and was patient in the second as games initially went by way of serve.
Donskoy struggled to muster a break point as Cilic comfortably doubled his lead, but he dropped serve for the first time in the third as his opponent attempted a comeback.
It proved to be just a momentary lapse, though, as the Croatian stormed back with two breaks of his own to continue his quest to win back-to-back crowns at Flushing Meadows.