Bartoli, seeded first and playing the day's first match, was defeated by Peng Shuai 6-0, 1-6, 6-4. Cibulkova, seeded second, dropped a 2-6, 6-4, 6-4 decision to Urszula Radwanska in the final match on Tuesday's schedule.
Peng lost just six points on serve in the third set. Bartoli only dropped 10 but Peng parlayed four into the sole break of the set.
Radwanska battled Cibulkova for 2 1/2 hours but had three second-set breaks to even the match and two more to finish the upset in the third.
Francesca Schiavone was a 6-2, 4-6, 6-3 winner over Lourdes Dominguez Lino. It was the second time in three days Schiavone came out ahead of Dominguez Lino. They played Sunday in the finals of the Morocco Grand Prix.
Defending champion Kaia Kanepi moved into the second round with a 6-4, 6-3 decision over Kristina Mladenovic.
Also Tuesday, as the first round wrapped up, Romina Oprandi beat Kiki Bertens 6-3, 6-3; Galina Voskoboeva defeated Sofia Arvidsson, Estrella Cabeza Candela took out Aravane Rezai 5-7, 6-1, 6-3; and Monica Niculescu ran part Tamira Paszek.