Qualifier Varvara Gracheva earned her first career top-five win by beating 2022 Wimbledon and US Open finalist Jabeur 6-2 6-2 in only 67 minutes on Friday.
Fifth seed Caroline Garcia also crashed out, losing 6-2 6-3 to 74th-ranked Sorana Cirstea, who also recently beat the Frenchwoman at Indian Wells.
Bianca Andreescu came from a set down to beat seventh seed Maria Sakkari 5-7 6-3 6-4 in a match that lasted over three hours.
Andreescu displayed some of the form that saw her lift the 2019 US Open title, fighting back from a set down and proving composed in the big moments.
The Canadian, who is ranked 31st, will take on 2020 Australian Open champion Sofia Kenin in the third round.
Reigning Australian Open champion Aryna Sabalenka, the second seed, had few problems against Shelby Rogers, winning 6-4 6-3 in one hour and 17 minutes. Sabalenka will next face 31st seed Marie Bouzkova.
Indian Wells champion Elena Rybakina beat Anna Kalinskaya 7-5 4-6 6-3, and Petra Kvitova eased past compatriot Linda Noskova 6-3 6-0.
Ninth seed Belinda Bencic dropped just two games as she cruised past Leylah Fernandez 6-1 6-1, and will face Ekaterina Alexandrova next as the 18th seed needed three to get past Taylor Townsend.
Veronika Kudermetova was eliminated by Marketa Vondrousova 6-4 6-2, who goes up against Karolina Pliskova in round three after Pliskova eased past Wang Xinyu in straight sets.
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