The No.2-seeded Li was strong on serve - she held eight of her nine service games - and was sharp on the return too, breaking Cornet four times in the match. She won in an hour and 24 minutes, 62 64.
"I was pretty nervous at the end, because the 4-3 and 5-3 games were pretty easy, and then the 5-4 game was pretty long," Li said. "I got a little bit tight, but I'm glad I could finish the match at the end."
After winning 20 of her first 24 matches of the year, Li had some struggles during the European clay court season, winning just two of five matches - she lost first round in Madrid (to Madison Keys), third round in Rome (to Jelena Jankovic) and second round at Roland Garros (to Bethanie Mattek-Sands).
So how did Li feel after getting over the first hurdle here? "Pretty good - at least I'm still in the tournament!" she said. "I'm happy to win my first match on grass and I'm looking forward to tomorrow."
"She's always tough," Li said. "It's a big challenge. She has been much, much better on grass courts and hardcourts. I think I've played her twice - and I don't think I've beaten her. So we'll see."
Li and Bartoli have played twice before but they are actually tied in their head-to-head, 1-1 - but it isn't a surprise Li may have forgotten about the one victory. Bartoli won their first meeting in the final of Monterrey in 2009, 64 63, and Li won their second meeting in the early rounds of Dubai in 2010, 36 75 60 - Li barely won that one, trailing 63 52 before winning 11 games in a row to sneak the victory out.
Li will be trying to reach the quarterfinals of Eastbourne for the first time in her career. She has fallen before the quarters in all four of her previous appearances, in 2008 (losing to Nadia Petrova in the second round), 2009 (losing to Agnieszka Radwanska in the second round), 2010 (retiring against Elena Baltacha in the first round) and 2011 (falling to Daniela Hantuchova in the second round).
Just a few weeks ago, Li went into the French Open as one of the favorites, or at least dark horses, for the title - but she was bundled out in a very difficult match-up against Mattek-Sands, 57 63 62.
"It was very tough conditions, coming back to the court three times, but for both of us it was the same," Li said that day. "I was surprised with the way she was playing, the way she was hitting the ball - I have to say well done to her, and good luck to her in the next round. She played really well today."
Mattek-Sands would eventually make it to the fourth round before falling to Maria Kirilenko.