The 18-year-old, who sat her A-Levels just two months ago, overcame her Czech opponent 6-2 6-4 having been a late wild card entry into the tournament.
It follows on from her first-round win against Vitalia Diatchenko and means she is now Britain’s last woman standing in the singles at the All England Club. The world No 338 will now face Sorana Cirstea after the Romanian beat 12th seed Victoria Azarenka 7-6 3-6 6-4.
Raducanu had showcased her impressive serve early on as she claimed the first set 6-2, but found herself three love down in the second amid a fightback from the world No 42 Vondrousova, who was runner-up at the 2019 French Open.
The Grand Slam debutante held her nerve and clawed her way back to three games apiece, eventually securing a crucial break courtesy of a double fault to earn a 5-4 advantage before serving out for a landmark victory in one hour and 12 minutes.
In sealing a place in the next round Raducana will earn £115,000, almost quadruple her career earnings heading into the match having only made her debut on the WTA Tour in June.