Czech Pliskova, who had a first-round bye, slammed down 11 aces but also committed nine double faults in a 7-5 6-4 defeat to Russia's Veronika Kudermetova.
Australian Open champion Kenin also struggled to get going after the COVID-19 layoff, losing 6-1 7-6(7) to France's Alize Cornet, who beat American wildcard Catherine McNally 6-0 6-4 in the opening round, dropping just 10 points in the first set.
"It didn't feel like I had any rhythm," said Kenin. "I don't know why I let that happen.
"I literally couldn't feel the ball, like literally two sets. I don't even know how I came back, to be honest.
"It was really frustrating."
Marketa Vondrousova continued her run of poor form as the Czech 10th seed lost 6-3 6-7(3) 6-4 to German qualifier Laura Siegemund in a first-round clash.
2019 French Open finalist Vondrousova, who also made a first-round exit at the WTA Tour's restart in Palermo, was up a break 4-2 in the third and looking set for victory until Seigemund swept the last four games.
Estonian 12th seed Anett Konaveit, coming off a runner-up finish in Palermo, moved into the second round with a 6-3 6-1 win over Russian lucky loser Daria Kasatkina, while 14th seed Elise Mertens of Belgium thumped Swede Rebecca Peterson 6-0 6-2.
In the men's draw, Greek fourth seed Stefanos Tsitsipas eased to a 6-1 6-3 second-round win over South Africa's Kevin Anderson while seventh seed David Goffin sailed past Croatia's Borna Coric 7-6(6) 6-4 into the third round.
Ninth seed Diego Schwartzman was a 7-6(2) 6-3 first-round winner over Norway's Casper Rudd while 11th seeded Russian Karen Khachanov topped Kazakhstan's Alexander Bublik 6-4 6-4.
Bulgarian 14th seed Grigor Dimitrov disposed of Frenchman Ugo Humbert 6-3 6-4.