Play didn't begin until almost 6:30pm after rain throughout the day, but once it cleared the No.9-seeded Jankovic was the first to move through, dispatching the American qualifier comfortably, 60 64.
"It was very difficult for all of us to wait around and just keep standing by," Jankovic said. "You didn't know when you were going to go on the court and you just had to be ready all the time and wait.
"But when I came out on court I played quite well. The court was slow because it was quite humid out there and there was a lot of rain. The balls were quite heavy and the overall play was quite heavy. But I got used to it, adjusted to it quite well, and I think I did a great job during the match today."
It was a stark contrast to Jankovic's previous two rounds - she needed almost three hours to beat Melanie Oudin in the first round, then had to save two match points to beat Caroline Garcia second round. But no matter the score the former World No.1 ended up with the win every time and has now won 12 of her last 14 matches, the losses coming to Svetlana Kuznetsova and Maria Sharapova.
"This is a new year and so far I think I'm doing pretty well and I think I have the confidence," Jankovic commented. "Like I've said before, I'm working very hard every day just trying to get to another level and become a better player overall. My goal is to get back to the top rank where I was before.
"But first of all, I want to play good tennis. That's what I'm striving for every day, and then the results will come. I have to fight every time I step on the court. Sometimes I have ups and downs but I have to cut down on those and when I get myself going out there, I have to stay there as long as I can."
"I was really excited to get out there and I felt like I played really well - it's unfortunate that she had to retire," Bouchard said after the match. "I thought she was serving pretty well, but we had some points where she wasn't running for the balls. I thought the court was pretty slippery out there so I kind of didn't run for some of the balls either, but she had like big tape on her leg, and I saw that.
"It's much better to win with a full match, but I'm excited to be here for tomorrow."
And how did Bouchard deal with the rain delay? "I slept - took a nap in the middle of the day," she said. "It was peaceful with the rain. It makes you fall asleep. But I got here at 5, so a few hours before going on, and everyone's very accomodating here. They had games for us and stuff, so it was fun."
Two other quarterfinal spots were snapped up on Thursday, with Stefanie Voegele upsetting No.10 seed Julia Goerges, 36 61 63, and No.2 seed Caroline Wozniacki advancing past Andrea Petkovic earlier on via walkover, after the German had to withdraw from the tournament due to a calf injury.
Both Jankovic against Bouchard and Wozniacki against Voegele will be first-time encounters.
The four third round matches from the top half of the draw were cancelled due to the rain. All four of those matches plus the four quarterfinals will take place on a very packed Friday schedule.