An American teenager and Russian veteran both advanced to the Grand Slam tournament's fourth round on the ladies side of the draw.
Stephens reached the fourth round by beating Mathilde Johansson of France 6-3, 6-2. Of the eight teenagers in this year's draw, the 19-year-old Stephens was the only one to even reach the third round.
"I'm excited because now I'm going to have more Twitter followers," Stephens said.
Sharapova has won three major titles in her career, but she still needs to win at Roland Garros to complete a career Grand Slam.
The 13th-seeded Ivanovic, a former top-ranked player who won the French Open title in 2008, committed 37 of her 40 unforced errors in the final two sets. Errani had only 18.
"In the third set I was creating a lot of opportunities and missing a lot of easy, easy finishing balls," Ivanovic said. "That's something that I'm not really happy about."