The No.14-seeded Jankovic dropped the first set and came within two points of losing serving at 4-5, 30-all in the third set, but her consistency was just too much in the end and she advanced, 36 75 75.
"I wasn't happy with the way I served today - there were a lot of breaks - but I was really happy with my returns today," Jankovic said afterwards. "I'm not sure why we had trouble serving today. Maybe it was the wind, my toss was all over the place, and I wasn't too happy with my game overall, but I'm happy with the way I fought. She's an up-and-coming player with a bright future, so I'm happy to win."
Jankovic leads Vinci in their head-to-head series, 4-2, though Vinci has won two of the last three.
"We've had a lot of tough matches," Jankovic said. "She has a different style of play from most of the girls. She hits a lot of slice, she has a lot of variety, she comes to the net a lot. We know each other well and we've played a few times this year too, so it's going to be a really tough match tomorrow.
"I'll just go out there and try to execute my shots and play the right tactics, and we'll see."
"Today I had a little bit of trouble serving sometimes, but overall I felt better than I did in my first match," Azarenka said. "I was doing everything I wanted to do. I feel there's still a lot more improvements I can make with the execution and a little bit more consistency, but it's coming along. It's getting there.
"What's important is that it was better than the other match. That's how I like to build up. From Canada, I feel good. Physically I feel good. I'm ready to go. My movement and everything is there. So it's just a matter of keeping on playing matches, keeping on getting competition in, and that's it really."
"It's a great opportunity to play against each other and see the difference from what we had two years ago," Azarenka said. "Either player I haven't played in a while. It's going to be interesting to play either one of them just to see where we're at. Whoever it is, I'm obviously going to try to do my best."
Wozniacki ended up winning that encounter with Kvitova later on in the day in three sets, 36 62 63.