Defending champion Sharapova was given a scare by China's Zheng Jie, recovering from a 4-1 deficit in the second set to win 6-1 7-5, while third seed Azarenka was pushed even harder before winning a three-setter against Frenchwoman Alize Cornet.
Azarenka's 4-6 6-3 6-1 victory put her on collision course with former champion Francesca Schiavone who ended the hopes of another home favourite with a 6-2 6-1 beating of Marion Bartoli.
With women's favourite Serena Williams enjoying a day off after motoring through to the last 16 on Friday, two American women took their chance to grab some of her limelight.
Sloane Stephens, 20, emulated her run to last year's fourth round with a three-set victory over New Zealand's Marina Erakovic while unseeded Bethanie Mattek-Sands also survived a three-setter against Argentine Paula Ormaechea.
The focus shifted to the men's draw later when Rafael Nadal was up against Italian Fabio Fognini, hoping to rediscover top form after a difficult first week of patchy form and rain, while top seed Novak Djokovic was taking on Grigor Dimitrov.
Despite the pleasant conditions, the day began in stormy fashion on Suzanne Lenglen court where 13th seed Kei Nishikori became the first Japanese man for 75 years to reach the fourth round at the claycourt slam.
His four-set victory over Benoit Paire, one of seven Frenchmen to reach the third round, saw his opponent given a penalty point for receiving coaching, prompting loud boos and jeers from the crowd packed on to court.
Paire had been on set point at the time and after arguing with the umpire and a tournament rules official he calmed down enough to take the set before losing 6-3 6-7(3) 6-4 6-1.
"I'm sure that if it was a top-five (player), they would never have done that, never taken the decision to say 'warning', 'penalty point' at that moment," the 24-year-old Paire told reporters.
"They would never do it because they know full well that you just can't do that sort of thing."
While Sharapova always looked capable of turning around her second-set deficit against Zheng, Azarenka looked in more trouble as she was knocked off her stride by Cornet.
Belarussian Azarenka, the Australian Open champion, eventually found her range to keep her challenge for a first French Open title on course.
"She's a machine, a juggernaut," Cornet told reporters. "She plays the same from the first to the last point."
