Australian second seed Barty overcame a horrible start to oust 80th-ranked Zarina Diyas of Kazakhstan 1-6, 6-3, 6-2.
Barty made 19 unforced errors to drop the first set in 28 minutes, but took the last three games in the second set and broke in the third and seventh games of the final set to advance.
"I was really pleased to be able to solve this riddle," Barty said.
Pliskova, a 2016 US Open runner-up who has a chance to finish the Flushing Meadows fortnight as world number one, held off 138th-ranked Czech qualifier Tereza Martincova 7-6 (8/6), 7-6 (7/3) after an hour and 46 minutes.
"It's tough to play Tereza," Pliskova said. "We never played and especially tough to play in the first round.
"Not my best performance today for sure, and she made some great shots."
Japanese seventh seed Nishikori reached the men's second round 6-1, 4-1, when 205th-ranked Argentine qualifier Marco Trungelliti retired with a back injury after 47 minutes.
"I played great tennis from the beginning," Nishikori said. "I'm happy with the way I played."
Russian fifth seed Medvedev, coming off an ATP title at Cincinnati and runner-up efforts at Montreal and Washington, defeated India's Prajnesh Gunneswaran 6-4, 6-1, 6-2 in just 85 minutes.
"I can't say I'm feeling amazing about my game but to win by that score in the first round is great," Medvedev said. "I hope I can continue to play well."
Top-seeded defending champion Novak Djokovic of Serbia faced Spain's Roberto Carballes Baena in a later match at Arthur Ashe Stadium.
Serena Williams opens her quest for a 24th Grand Slam singles crown against Russia's Maria Sharapova, a five-time Slam winner, in the night feature before 20-time Grand Slam champion Roger Federer meets Indian qualifier Sumit Nagal.
Williams is 19-2 all-time against Sharapova with 18 consecutive triumphs.
"It had to start with my serve," Barty said of her fightback in the opening match on Arthur Ashe. "I wasn't giving myself enough chances on my serve. It was just start again, break it down, figure it all out.
"Zarina was able to put me in difficult positions. I just kept making good shots. I felt like I had good control and could put it in difficult spots on the court."
Pliskova and her compatriot exchanged breaks of serve through the first six games, Martincova later coming within two points of the set before Pliskova rallied.
Pliskova forehand winners took the last two points of the first tie-breaker and she won the last four points in the second, smashing a service winner to claim the match.
"Not happy that I lost three breaks of serve in a row. That's not possible for next time," Pliskova said. "I'm happy I could get through."
Pliskova, Barty, Wimbledon champion Simona Halep and top-ranked defending champion Naomi Osaka could top the rankings after the US Open.
Osaka and Halep must win the title. Pliskova needs to at least reach the quarter-finals. Barty is the front runner, defending fewer points from last year's Open than Osaka.
Williams, seeking her seventh US Open title, is chasing her 24th Grand Slam singles crown, which would match Margaret Court's all-time record.
The 37-year-old American is 0-3 in Slam finals since becoming a mother two years ago, her last Slam crown coming at the 2017 Australian Open while pregnant.
"Ready in NY for the US Open," Williams posted Monday morning on Instagram. "I'm on tonight."
Williams has never played Sharapova at the US Open, which the Russian won in 2006.
US Open results on Monday (x denotes seeding):
Novak Djokovic (SRB x1) bt Roberto Carballes Baena (ESP) 6-4, 6-1, 6-4
Denis Kudla (USA) bt Janko Tipsarevic (SRB) 3-6, 6-1, 7-6 (7/5), 6-1
Dusan Lajovic (SRB x27) bt Steve Darcis (BEL) 7-5, 6-3, 6-3
Jenson Brooksby (USA) bt Tomas Berdych (CZE) 6-1, 2-6, 6-4, 6-4
Nikoloz Basilashvili (GEO x17) bt Marton Fucsovics (HUN) 3-6, 6-4, 6-2, 3-6, 6-3
Daniil Medvedev (RUS x5) bt Prajnesh Gunneswaran (IND) 6-4, 6-1, 6-2
Dan Evans (GBR) bt Adrian Mannarino (FRA) 6-4, 6-3, 2-6, 6-3
Cristian Garin (CHI x31) bt Christopher Eubanks (USA) 3-6, 7-6 (7/5), 6-4, 6-7 (4/7), 6-3
Alex de Minaur (AUS) bt Pierre-Hugues Herbert (FRA) 6-4, 6-2, 6-7 (6/8), 7-5
Bradley Klahn (USA) bt Thiago Monteiro (BRA) 6-3, 6-2, 6-3
Kei Nishikori (JPN x7) bt Marco Trungelliti (ARG) 6-1, 4-1 retired
Venus Williams (USA) bt Zheng Saisai (CHN) 6-1, 6-0
Rebecca Peterson (SWE) bt Monica Puig (PUR) 6-3, 6-3
Dayana Yastremska (UKR x32) bt Monica Niculescu (ROM) 6-4, 1-6, 6-2
Johanna Konta (GBR x16) bt Daria Kasatkina (RUS) 6-1, 4-6, 6-2
Margarita Gasparyan (RUS) bt Priscilla Hon (AUS) 7-6 (7/4), 6-4
Ekaterina Alexandrova (RUS) bt Samantha Stosur (AUS) 6-1, 6-3
Ons Jabeur (TUN) bt Caroline Garcia (FRA x27) 7-6 (10/8), 6-2
Aliaksandra Sasnovich (BLR) bt Jennifer Brady (USA) 6-1, 4-6, 6-0
Mariam Bolkvadze (GEO) bt Bernarda Pera (USA) 6-3, 5-7, 6-4
Karolina Pliskova (CZE x3) bt Tereza Martincova (CZE) 7-6 (8/6), 7-6 (7/3)
Hsieh Su-Wei (TPE x29) bt Jana Cepelova (SVK) 6-4, 5-7, 6-3
Petra Martic (CRO x22) bt Tamara Zidansek (SLO) 6-4, 4-6, 6-1
Ana Bogdan (ROM) bt Harriet Dart (GBR) 6-3, 6-1
Iga Swiatek (POL) bt Ivana Jorovic (SRB) 6-0, 6-1
Anastasija Sevastova (LAT x12) bt Eugenie Bouchard (CAN) 6-3, 6-3
Kristina Mladenovic (FRA) bt Angelique Kerber (GER x14) 7-5, 0-6, 6-4
Fiona Ferro (FRA) bt Daria Gavrilova (AUS) 6-3, 6-4
Alison Van Uytvanck (BEL) bt Viktoria Kuzmova (SVK) 6-4, 6-4
Lauren Davis (USA) bt Johanna Larsson (SWE) 7-5, 6-2
Ashleigh Barty (AUS x2) bt Zarina Diyas (KAZ) 1-6, 6-3, 6-2