Down 5-4 in the second set, Pegula couldn't hold serve, giving Kalinskaya the set. In the third, Pegula went down 3-0 quickly and couldn't fight her way back into the match.
The day was far better for another American, second-seeded Emma Navarro, who needed 93 minutes to defeat Russian qualifier Anna Blinkova 6-4, 6-1. Navarro also reached the quarters in Strasbourg in 2023.
In the next round, she'll face Brazil's Beatriz Haddid Maia, the ninth seed, who topped Ashlyn Krueger 7-6(3), 6-3.
The day's other winner was Danielle Collins, the runner-up to Madison Keys in Strasbourg last season. She ousted Great Britain's Emma Raducanu 4-6, 6-1, 6-3 in the first meeting between the former Top 10 players.
Collins needed two hours, 20 minutes to pull off the clay-court win and set up a quarterfinal match with Kalinskaya.
Grand Prix Sar La Princesse Lalla Meryem
Second seed Camila Osorio of Colombia outlasted Russia's Kamilla Rakhimova 4-6, 6-2, 6-3 to move on to the quarterfinals in Rabat, Morocco.
It was a match littered with break points, with Osorio converting 7 of 11 chances and her opponent 5 of 13.
The two other seeded players in action also moved on in three sets. Fourth seed Ann Li defeated fellow American Hailey Baptiste 6-4, 6-7(5), 7-5, while No. 10 Jessica Bouzas Maneiro of Spain eliminated Burundi's Sada Nahimana 6-4, 4-6, 6-1.
Katie Volynets, the ninth seed, fell to Australia's Maya Joint in straight sets. Also moving to the quarterfinals were Maria Mateas, Jaqueline Cristian of Romania and Australia's Ajla Tomljanovic.