Belgian 47th-ranked Van Uytvanck triumphed 5-7, 6-2, 6-1 for her first-ever win over a top 10 opponent.
The shocks at the World Cup have made their way over to Wimbledon, with defending women's champion Garbine Muguruza and last year's men's finalist Marin Cilic the latest casualties in the second round.
No. 7 Karolina Pliskova is the other top-eight-seeded woman left in the draw.
The Belgian No.3 returns to the second week of a Grand Slam for the first time since a similarly shocking run to the quarterfinals of the French Open in 2015, and prevented the Estonian from reaching the round of 16 at the first three majors this season.
While Van Uytvanck's reward was a place in the Wimbledon third round for the first time, Muguruza was off to join the snaking checkout queue - a line that already includes beaten Grand Slam champions Caroline Wozniacki and Petra Kvitova.
With a second chance to serve out the set, the defending champion was quick to build a 40-0 lead and a forehand that just clipped the baseline put the third seed in front after 48 minutes of play.
"She played big, took risks and it worked for her but my level was not where I wanted it to be", said the deposed champion.
When Garbine Muguruza clutched her temple with both hands and shook her head repeatedly, she laid bare the throbbing pain racing through her body as her Wimbledon title defence was hijacked by a little-known Belgian on Thursday.
Johanna Konta, a semi-finalist at her home grand slam previous year, went down 6-3 6-4 to an impressive Dominika Cibulkova.
"I didn't know but I don't see a clock here".
But she clung on and went on win the next 10 games, locking out her opponent from the contest entirely.
Madison Keys has become the latest top-10 seeded woman to lose at Wimbledon after her comeback fell short.
"I was thinking about every single point when I was serving for the match", Kerber said. I think this was the best thing that I did, I didn't panic.
"Today when we came back, obviously he served two good service games in that third set, came back two sets to one", Cilic told reporters.
"I would love to be in the second week for the first time for me in Wimbledon", she added.
British hopes were dashed when 22nd seed Johanna Konta went out, losing to former world No. 4 Dominika Cibulková, 3-6, 4-6.
Three years ago in Rio, Bernardes, said Nadal, forced him to change his shorts - which were upside down - on court instead of somewhere more private. "Of course it was a tough draw today and today I can only be happy with my performance". That's why she could develop that kind of level.
French Open champion Halep reached the 3rd round with a 7-5, 6-0 win over China's Zheng Saisai and next plays Hsieh Su-Wei of Taiwan.