The odds were stacked in Radwanska's favor going into the match - she had won the pair's last four meetings in straight sets, and Vesnina had a dubious 0-20 lifetime record against Top 4 players.
All of that almost went out the window this time, as the No.32-seeded Vesnina went up a break twice in the first set and once more early in the second set. But the No.3-seeded Radwanska kept coming back each time, eventually grinding the match out in straight sets in an hour and 41 minutes, 75 63.
"The service games were really tricky today because the wind was coming from one side, so we couldn't really break through that," Radwanska said. "Especially the last game was really tough, but suddenly I started to serve much better, a couple of aces, and that was the match. It was tough.
"A few aces at the end of the match doesn't happen often, especially when you're down 0-40 and getting a little nervous and shaking, but I think in the important moments I had some good shots."
Radwanska was very complimentary of Vesnina's play when she was asked about it after the match.
"She was really hitting the ball very hard, using the wind very well and serving very well," Radwanska said. "I had a lot of trouble with her today. Especially the first set today was a pretty difficult one."
Radwanska and Svitolina will be playing against each other for the first time.
"To be honest I don't know much about her," Radwanska said of Svitolina. "It's always challenging playing someone you don't know. And she made the fourth round, so she must be playing good tennis.
"She must have beaten some seeded players along the way too, so I'll have to be ready."