Japanese seventh seed Nishikori, the 2014 US Open runner-up and a semi-finalist in 2016 and 2018, defeated 108th-ranked American Bradley Klahn 6-2, 4-6, 6-3, 7-5 after two hours and 44 minutes.
"Looking forward to the next one," Nishikori said. "Hopefully I can continue to play good tennis."
Next in Nishikori's path will be either Australian Alex de Minaur or Chilean 31st seed Cristian Garin.
Czech third seed Pliskova, seeking her first Grand Slam title and the world number one ranking, ousted 202nd-ranked Georgian qualifier Mariam Bolkvadze 6-1, 6-4 in 66 minutes.
"It was a solid performance," Pliskova said. "I didn't have to play the best today."
Pliskova, the 2016 US Open runner-up, was pleased with her serve, winning 26 of 29 first-serve points and connecting on 67 percent of first serves.
She will next face either Tunisia's Ons Jabeur or Aliaksandra Sasnovich of Belarus.
Top-ranked defending champion Novak Djokovic, 20-time Grand Slam winner Roger Federer and six-time US Open champion Serena Williams are set for later matches at Arthur Ashe Stadium.
US eighth seed Williams, seeking a 24th career Grand Slam title to match the all-time record won by Margaret Court, faces 17-year-old US wildcard Caty McNally.
Williams, 37, had won her first Slam title at the 1999 US Open and reached her second Flushing Meadows final before 121st-ranked McNally was born.
Djokovic, winner of four of the past five Slam titles and 16 in all, meets Argentina's 56th-ranked Juan Ignacio Londero in the other night feature. The Serbian star is trying to become the first back-to-back Open champion since Federer's run from 2004-2008.
Swiss third seed Federer, who lost to Djokovic in last month's epic five-set Wimbledon final, meets 99th-ranked Bosnian Damir Dzumhur. Federer, 38, hasn't fallen in a Slam second round since 2013 at Wimbledon.
- 'Lost focus' -
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Nishikori, who could face Federer in the quarter-finals, broke twice and took the first set in 28 minutes.
Klahn battled back and broke in the 10th game to claim the second set, but Nishikori dominated from there to a 5-1 lead in the fourth set.
Klahn saved a match point in the seventh game to start a run where he won 12 of 15 points. He denied another Nishikori match point and held serve to 5-5.
But Nishikori held again and then seized three more match points on Klahn, the American finally succumbing on the last of them when he smacked a backhand beyond the baseline.
"A little bit of lost focus after 5-1," Nishikori said. "He started playing better too. I knew it was going to be a tough one because he has a great serve."
Pliskova needs to reach at least the quarter-finals to have a chance at becoming world number one after the US Open while top-seeded defending champion Naomi Osaka of Japan and reigning Wimbledon champion Simona Halep of Romania must win the title.
French Open champion Ashleigh Barty, the second seed from Australia, has the inside track in the chase for number one, thanks to Osaka defending more points from her win last year.
Barty was set to play 73rd-ranked American Lauren Davis later. The Aussie could meet Serena Williams in the quarter-finals.