The 12th-seeded Kirilenko lost in the fourth round at Roland Garros in 2010 and 2011.
She trailed 4-1 at the start against Mattek-Sands, who stunned 2011 French Open champion Li Na in the second round.
But Mattek-Sands' lead began slipping away, and while ahead 5-4, she asked for medical attention. From there, Kirilenko won four games in a row.
Kirilenko, who is engaged to two-time NHL MVP Alex Ovechkin of the Washington Capitals, also was visited by a trainer, getting a massage on her right shoulder in the second set.
Kirilenko held on, though, and faces two-time major champion Victoria Azarenka next.