The fifth seed won 7-5 6-3 7-5 to the delight of a patient contingent of Japanese fans who had sat wrapped up against the drizzle on Court Three through a lengthy break between the second and third sets.
Nishikori, 26, beat Kuznetsov in straight sets in the second round at the French Open and once again the swashbuckling Russian, 25, failed to find a way to counter the Japanese player's baseline aggression and solid defence.
He broke Nishikori's service in the third set after a first rain delay to go 3-0 up but lost his own after a second shorter pause and, racking up the unforced errors, never got back on top.
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Nishikori next meets ninth seed Cilic who beat him in the 2014 U.S. Open final. Although Cilic dashed his hopes of a first Asian men's grand slam title, Nishikori has a 7-3 advantage over the tall Croatian in head-to-heads.
(Reporting by Clare Lovell, editing by Ed Osmond)
