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.
"I think in the beginning, in the middle of that first set, I tried to feel the speed of her serve," Kudermetova said. "I tried to push every point on receiving. I think it was key. I tried to just keep going on her serve."
Australian Open champion Kenin also struggled to get going, losing 6-1, 7-6(7) to France's Alize Cornet, who beat American wildcard Caty McNally 6-0, 6-4 in the opening round, dropping just 10 points in the first set.
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"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."
It was the Frenchwoman's best win in two years, having last beaten a Top 10 player at the Coupe Rogers in Montreal back in 2018.
"I'm a fighter," she said after the match. "I'm always fighting, so that's nothing new, but tonight was tough because I was 6-1, 5-2 up with two match points."
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Last year's French Open runner-up 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.
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 Siegemund swept the last four games.
Estonian 12th seed Anett Kontaveit, 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 Ruud while 11th-seeded Russian Karen Khachanov topped Kazakhstan's Alexander Bublik 6-4, 6-4.
Fourteenth seed Grigor Dimitrov disposed of Frenchman Ugo Humbert 6-3 6-4. The Bulgarian is returning to full fitness following a spell out with coronavirus.
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