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The World No 1 won 6-2,6-4, 6-0 at the Arthur Ashe Stadium.
Djokovic announced his withdrawal from the year's last Grand Slam tournament on Twitter.
Coric signalled his return to full fitness from shoulder surgery and showed that he will be a threat at the US Open.
Petra Kvitova overcame a sluggish start and 10 double faults to beat Madison Keys 6-7(6), 6-4, 6-3 and advance to the women's singles final, where she will face Caroline Garcia, the first qualifier to reach the final of a WTA 1000 tournament.
In the men's section, world No. 1 Daniil Medvedev and fourth seed Stefanos Tsitsipas defused big-serving American threats Taylor Fritz and John Isner to reach the semifinals.
Taylor Fritz blasted his way to a 6-3, 6-2 win over Australian Nick Kyrgios while Cameron Norrie fought back to beat former world No. 1 Andy Murray 3-6, 6,-3 6-4 in an all-British clash.
Hurkacz, whose power is suited to grass courts, is third on the list of number of aces hit on the ATP Tour this year with 452 -- behind big-serving Americans John Isner and Reilly Opelka.
Djokovic and Nadal find themselves in different halves of the draw and they cannot face each other until the men's final on July 10.
The Pole hammered world No. 1 Daniil Medvedev 6-1, 6-4 to win the ATP 500 grasscourt tournament.
Wimbledon's move to ban them from the tournament which begins later this month prompted the men's ATP and women's WTA Tours to strip the grasscourt Grand Slam of its ranking points.