Frenchwoman Bartoli was the highest-ranked player to suffer an upset as the women's second seed lost her second-round match against Sofia Arvidsson of Sweden 6-3 6-0.
Also eighth seed Lucie Safarova was knocked out in straight sets after losing 6-4 6-4 to fellow Czech Klara Zakopalova.
Meanwhile, in the men's event, third-seeded Troicki's bid for a third successive final appearance came to an end as the 2010 champion and last season's runner-up was defeated 6-1 3-6 6-2 by world number 112 Malek Jaziri.
Another seed to be knocked out was number six Denis Istomin, who went down 4-6 6-4 6-3 to Lukas Rosol in the second round.
Tatsuma Ito did manage to progress through - the only one of the three men's seeds in action to do so - but the number eight from Japan had it far from easy before finally seeing off qualifier Konstantin Kravchuk 7-6 (9/7) 2-6 6-3.
Not all of the seeded players found it tough going, though.
Third seed Caroline Wozniacki cruised past Urszula Radwanska 6-1 6-3, while fifth seed Dominika Cibulkova, the defending champion was a similarly convincing victor over Tsvetana Pironkova, winning 6-2 6-3.
Seventh-seeded Maria Kirilenko also had few problems seeing off Russian compatriot Elena Vesnina 7-5 6-1 to join Wozniacki and Cibulkova in the quarter-finals.
In other men's matches, Ivo Karlovic, Jerzy Janowicz, Flavio Cipolla and Edouard Roger-Vasselin won their first-round ties, while in the women's event, qualifier Valeria Solovieva progressed through to the second round.