Ivanovic was shaky throughout the 6-7 (2-7), 7-6 (7-3), 10-8 match that lasted 3 hours and 24 minutes. Dechy, ranked 97th, twice had Ivanovic at match point, including one in which Ivanovic's forehand shot hit the net cord and just went over the net for a winner.
It wasn't until the 18th game of the third set that Ivanovic was able to cash her fourth attempt at a match point and advance to the third round.
Fourth-seeded Svetlana Kuznetsova and No. 6 Serena Williams were much more solid in their Wednesday matches. Kuznetsova took out Kateryna Bondarenko, 6-2, 6-3, and Williams dispatched Urszula Radwanska, 6-4, 6-4.
In other second-round matches, 11th-seeded Marion Bartoli defeated Tatiana Perebiynis, 6-2, 7-5; No. 15 Agnes Szavay beat Monica Niculescu and 18th-seeded Nicole Vaidisova was a 6-2, 0-6, 6-4 winner over Samantha Stosur.
Also Wednesday, Jie Zheng advanced into a third-round match with Ivanovic and Casey Dellacqua and Bethanie Mattek won second-round matches.