Sharapova, seeded 12th, was beaten by Kimiko Date Krumm, 7-5, 3-6, 6-3. Date Krumm, who turns 40 Tuesday, advanced to the second round by cashing in five of six break-point opportunities.
Jankovic, the No. 3 seed, headed to the third round with a 6-4, 6-1 victory over Alona Bondarenko on the strength of a receiving game in which she took 59 percent of the points off Bondarenko's serve.
No. 6-seeded Agnieszka Radwanska eased past Olga Govortsova 6-2, 6-3 in the day's other second-round match.
No. 15-seeded Nadia Petrova joined Sharapova as a first-round upset victim, losing 7-5, 6-4 to qualifier Roberta Vinci.
No. 10-seeded Svetlana Kuznetsova was down 3-4 in the first set when Agnes Szavay suffered a left thigh strain and retired. Among other seeded players, No. 11 Marion Bartoli defeated Yanina Wickmayer 6-4, 6-4; 13th-seeded Shahar Peer slipped by Timea Bacsinszky 5-7, 7-5, 6-4; and No. 14 Aravane Rezai defeated Polona Hercog 6-2, 7-5.
Other winners Monday were Alexandra Dulgheru, Ana Ivanovic, Yaroslava Shvedova, Sara Errani, Julia Goerges and qualifier Coco Vandeweghe.
Celebrity Families of 2014 [PHOTOS]