However, outside of that tournament and this one, she has only amassed three Grand Slam wins.
Her partner Greet Minnen — who is also a Belgian tennis player, ranked 546th — has been courtside throughout the tournament.
"We're a good team," Van Uytvanck said. "She's also a tennis player. ... So it's really good she understands the game."
There was also a timely element to Van Uytvanck achieving her career-best performance at Wimbledon.
While she was on court, tens of thousands of people had begun participating in a parade celebrating Britain's LGBT community in the city center.
With a fourth-round match against 14th-seeded Daria Kasatkina of Russia to come on Monday, Van Uytvanck wasn't ready for any celebrations.
"Somebody told me it's the Pride (parade) today," Van Uytvanck said with a laugh. "But I will just get some rest."
- AP