Bouchard recorded a 63 61 victory over Alisa Kleybanova, a former Top 20 player who was playing the first match of her full comeback from a leave from the tour to recover from Hodgkin's lymphoma.
"Obviously Alisa is a great player," Bouchard commented. "She has been very good, and I'm sure she will get back to being really good. I wasn't too sure what to be prepared for, but I felt like I was ready for anything. I was able to play really solid today. I was happy with how the match went out there."
Kleybanova was playing her first WTA-level event since Miami last March, though she has played at the ITF Women's Circuit level this year. "I was pretty excited to go out there," the Russian said. "I love playing on stadium court and being in front of the crowd - it's a great experience for me every time.
"Today I went out and tried to do my best, and I obviously did. But she played really well. There wasn't really much I could do at the moment, but it's always an experience for me. I'm not expecting it to be easy to come back and play unbelievable tennis after such a big break. So I'm just taking it one step at a time and I'm getting ready for my next tournaments right now. I'm just going to take the lessons out of this match but not think about it too much, and just look forward from here to the next matches."
Stosur, the No.12 seed, was the last player into the second round, wrapping up a 57 62 63 victory over Israeli qualifier Julia Glushko at 10:28pm. Stosur came back from a break down to win the third.
Also moving through later was No.3 seed Agnieszka Radwanska, who beat Yanina Wickmayer, 62 63. That was one of two second round matches on Tuesday, along with Dominika Cibulkova's upset over No.8 seed Angelique Kerber (read more here). The rest of the second round is on Wednesday.
Hingis was asked about the differences between playing doubles in her previous career and now.
"When I played before there were no deuce points like there are now - you always had advantage and deuce," she said. "I think that's the biggest difference, those key points that are really important, that you have to be ready on and try to do your best, like 120%, not just like 50%. That's the big key.
"Today and in the two matches last week, for me that's the big difference - you have to be spot on."