The 15-year-old defeated 28th seed Linda Fruhvirtova 6-2 0-6 6-4. She grew up playing tennis at a club near the renowned stadium.
I’m stunned, Klugman exclaimed. It felt great to win, and it was really emotional.
Amarni Banks and Sonay Kartal, two more British nationals, have advanced to the final qualifying round.
On Thursday, Klugman’s last qualifying match will be broadcast live on the Sport website and app, as well as BBC iPlayer. It is not anticipated that the contest will start before 12:30 BST.
Klugman, a 14-year-old junior Wimbledon competitor, took home the coveted Orange Bowl gold in Florida last year.
The world number 623 overcame Czech opponent Fruhvirtova, who is ranked 376 places above her, after losing the second set to love at Roehampton.
At 15 years and 122 days in 2019, current US Open champion Coco Gauff became the youngest Wimbledon qualifier in modern history.
The next time Klugman plays American world number 121 Alycia Parks on Thursday, she will only be eight days older.
Monday is Wimbledon’s opening day; the draw is held on Friday.