Mladenovic, a wild-card entrant, edged past seventh-seeded Julia Goerges 7-5, 5-7, 7-6 (7-4) in a match that took 2 hours, 42 minutes. Goerges won one more point (117-116) and both players had four breaks in the very tight match.
Each player had a third-set break in getting to the tiebreaker where Mladenovic was able to prevail.
Fifth-seeded Roberta Vinci rolled over Simona Halep 6-0, 6-3 in 52 minutes. Vinci had seven aces and saved all four of the break points she faced. She won two-thirds of the points on serve and 62 percent of the points overall. Vinci dropped just eight points in the first-set shutout.
Also Tuesday in the first round, Carla Suarez Navarro defeated Monica Niculescu 6-3, 7-6 (7-3); Alize Cornet outlasted Sofia Arvidsson 6-3, 4-6, 6-0; and Stefanie Voegele topped Tsvetana Pironkova 6-4, 6-2.