The eighth-seeded Serb did little right on Court Suzanne Lenglen, converting only two of her five break points and making 20 unforced errors.
Before the final game of the first set, Ivanovic called for a trainer to look at her neck. Azarenka then held to take the lead, and broke Ivanovic’s serve in the first and third games of the second set to take a 4-0 lead.
Ivanovic won her only Grand Slam tournament title at last year’s French Open.
The 19-year-old Azarenka lost in the fourth round at Roland Garros last year, and will next be playing in the quarterfinals of a Grand Slam tournament for the first time.
Maria Sharapova rallied again, moving into the fourth round by beating Li Na of China 4-6, 6-0, 6-4.
Sharapova is making her return to Grand Slam tennis after almost a year off due to a right shoulder injury. She lost the first set of her matches in the first and third rounds, and lost the middle set in the second round.
The three-time major champion needs only a title at Roland Garros to complete a career Grand Slam.
Dinara Safina had a much easier time on center court, advancing to the quarterfinals with a 6-1, 6-0 win over Aravane Rezai of France.
The top-seeded Safina won 11 straight games to close out the match. She has lost only five games through four rounds of the clay-court major, and has won four of the eight sets she has played at love.
“I’m just surprised that it’s really like five games that I lost before getting into the quarters,” Safina said. “It’s not a bad feeling, and I hope if I continue like this I can go a long way.”
Safina took over the No. 1 ranking this year, but has yet to win a Grand Slam title. She lost to Ivanovic in last year’s French Open final, and fell to Serena Williams in this year’s Australian Open title match.
But since taking over the top spot in the women’s rankings, Safina said things have been easier on her.
“It was too much pressure for me,” Safina said of the rise to the top. “It was always going on the court not to lose a match, and of course it’s always difficult to play when you step on the court and you’re afraid of losing.
“So I think once I go to No. 1 spot, I took it (off) my shoulders. Like, OK, I’m there where I wanted to be. Now I just want to go out there and play.”
No. 20 Dominika Cibulkova also reached the quarterfinals in the women’s draw at Roland Garros. The 20-year-old Slovak beat No. 29 Agnes Szavay of Hungary 6-2, 6-4 in a sloppy match that had a combined 17 winners and 66 unforced errors.
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