|US Open 2019|
|Venue: Flushing Meadows, New York Dates: 26 Aug – 8 Sep|
|Coverage: Live text and BBC Radio 5 Live Sports Extra commentary on selected matches on the BBC Sport website and app. Click here for Live Guide.|
The Japanese player was 5-1 up in the fourth set and had four match points before eventually overcoming the world number 108.
The 2014 finalist eased into a one-set lead and was 4-2 up in the second before Klahn fought back to level.
Nishikori reasserted control to secure victory in two hours and 43 minutes.
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Elsewhere, Croatian 12th seed Borna Coric withdrew from the competition with a lower back strain before he was due to play Bulgarian former world number three Grigor Dimitrov.
The 22-year-old, who reached the fourth round last year, tweeted: “The last couple of months were really tough because of the injury I had. For an athlete, the worst thing that can happen is an injury in the middle of the competition.
“It is never easy to withdraw but at this moment, my body is telling me to stop and assess the situation. So as hard as this decision is, I think it is smart in the long term.”