Cornet not only battled back from 62 52 down to push the second set to a tie-break, she also saved five match points in that tie-break - three from 6-3 down, then another two at 7-6 and 8-7 down - and she even rallied from 2-0 down in the third set to scrape past the No.15-seeded Ivanovic, 26 76(8) 64.
It wasn't an easy ending for Cornet herself though - serving for the match at 5-4 in the third set, she missed out on her first five match points - but she closed out the nail-biter on match point No.6.
Cornet has had somewhat of a revival over the last few weeks. In the two-and-a-half-year span between January 2011 and July 2013, she went 0-26 against Top 30 players - a difficult stat given she is a former World No.11. But since starting her summer hardcourt season in Washington DC two weeks ago she has gone 4-1 against Top 30 players, scoring wins over a No.28-ranked Sorana Cirstea, a No.22-ranked Elena Vesnina, a No.16-ranked Maria Kirilenko and now World No.14 Ivanovic.
In other first round matches later in the day, No.10 seed Caroline Wozniacki cruised past Peng Shuai, 61 61; No.13 seed Kirsten Flipkens won the first set but ended up falling to Vesnina, 36 61 63; No.14 seed Jelena Jankovic won a very tight three-setter against Sabine Lisicki, 76(5) 57 62; and Monica Niculescu, who got in as a lucky loser after Cirstea withdrew, outdid Yanina Wickmayer, 61 62.
Cirstea, who was coming off the biggest week of her career - reaching her first Premier-level final in Toronto, taking out three Top 10 players en route - had to withdraw with a left abdominal strain.
Jankovic's win over Lisicki could have been over a lot sooner, as the Serb served for the match at a set and 5-4, even going up 30-0 in that game. But Lisicki pushed it to a third before finally falling.
Lisicki was playing her first tournament since reaching the Wimbledon final, where she fell to Marion Bartoli. She was the first German to reach a Grand Slam final since Steffi Graf achieved the feat at Wimbledon 14 years ago in 1999. Lisicki hadn't played since Wimbledon due to a right wrist injury.