Australia's Stosur, holding the No. 5 seed, rolled past China's Peng Shuai 6-2, 6-2, while seventh-seeded Bartoli of France breezed by Czech qualifier Iveta Benesova 6-3, 6-2.
Li, the 2011 French Open champion, eliminated the Czech Republic's Lucie Safarova 7-6 (7-4), 6-4 in a 92-minutes effort on the indoor red clay court.
Defending champ Julia Goerges of Germany advanced to meet Stosur, rallying for a 5-7, 6-3, 6-4 win over Russia's Anastasia Pavlyuchenkova.
Other winners Tuesday included Andrea Petkovic, who returned from a three-month injury absence, German Angelique Kerber, Italian Francesca Schiavone, Hungarian qualifier Greta Arn and French qualifier Alize Cornet.
Notable deaths of 2014 [PHOTOS]