The No.2-seeded Li had some early trouble against Paula Kania, going down a break in the first set, but she rallied and eventually - and comfortably - made her way past the Polish qualifier, 7-5, 6-2.
"I took 10 days off," Li said when asked what she had been doing since that loss. "No racquet, no physio, I just stayed with my friend and took a vacation. And it felt pretty good. Afterwards I felt more fresh, because I felt the pressure during the French Open and I couldn't handle it anymore."
"I'm just happy to be able to play again," Azarenka, who had played just two matches since Australia due to a foot injury, said. "This is what I love to do. The best feeling is playing pain free - and that's what's important to me. Getting my game together and the timing is a long process, but the important thing is I'm here, and I'm 100%. My focus, desire and concentration are all there right now.
"I was just really happy to play. It's a beautiful court. It's a beautiful tournament."
Former Wimbledon winners Petra Kvitova and Venus Williams, who are in a third round collision course, also advanced, the No.6-seeded Kvitova cruising past Andrea Hlavackova, 6-3, 6-0, and the No.30-seeded Williams battling past María-Teresa Torró-Flor in an entertaining one, 6-4, 4-6, 6-2.
"It was great," Williams said. "My opponent played amazing. She was just playing so well and going for everything, so it was definitely a challenge today against someone who was playing inspired tennis."
But three seeds were not, starting with No.17 seed Sam Stosur and No.18 seed Sloane Stephens. Stosur, who has struggled at Wimbledon in recent years, fell to Yanina Wickmayer, 6-3, 6-4, while Stephens was outdone by Maria Kirilenko, who closed out a 6-2, 7-6(6) win on her sixth match point.
"Obviously Maria's a great player," Stephens said. "She's done well here in the past and I knew it was going to be tricky, but that's like every other Grand Slam first round match. She was just too good."
Stephens was the only player on the tour to reach the second week of every Grand Slam since the start of last year - and she was a quarterfinalist here last year - but it was just not to be this year.
"I'm sad my streak is broken, but obviously there's nothing I can do now," Stephens said.
"It feels like the end of the world now, but fortunately it's not."
And in perhaps the most dramatic match of the day, CoCo Vandeweghe - fresh off her first WTA title 's-Hertogenbosch - edged No.27 seed Garbiñe Muguruza, 6-3, 3-6, 7-5. Vandeweghe needed 13 match points to close out the French Open quarterfinalist, who double faulted on the unlucky 13th.