The top-ranked Australian took just over an hour and 20 minutes to take the 7-6 6-2 win over the Belgian. 

Van Uytvanck spurned two set points in the opening set before Barty closed out a tense tiebreak and broke her three times in the second set.

She now faces former world No.11 Alize Cornet, who stunned Wimbledon champion Angelique Kerber 6-4 6-1.

In her press conference after the victory, Cornet had praise for her upcoming opponent.

"She's a different player, a little bit like Kasatkina. I like this kind of player that shows different thing on the court: going to the net, slicing on the backhand side," she said.

"It's nice because I'm also a little bit this kind of player that does a lot of variation in my game. Definitely a very interesting match. I'm looking forward to it," Cornet said.

It will be the second time the two meet after Cornet came out on top in the first meeting back in the first round at the 2014 French Open.