Despite making a strong start, fourth seed Pliskova faltered and lost 1-6 6-4 6-4 to the world number 127 in the pair's last-32 match.
Boulter said: "I'm super-proud of myself today. I went out there and didn't feel great on court, and I worked so hard to battle and fight, and against a player like that it means so much to me, coming through that."
There was another major shock win for a British player later in the day as Jodie Burrage knocked out top seed Paula Badosa, the world number 169 triumphing 6-4 6-3 against a player who will be seeded fourth at Wimbledon.
Defending champion Jelena Ostapenko beat Ajla Tomljanovic 6-4 6-4 and two-time Wimbledon winner Petra Kvitova saw off Donna Vekic 6-1 7-6 (7-1), while Beatriz Haddad Maia's strong form on grass continued with a 6-4 3-6 6-3 victory over Estonian veteran Kaia Kanepi.
Brazilian left-hander Haddad Maia is coming off the back of title wins in Nottingham and Birmingham and stretched her winning run on grass to 11 matches.
There were also wins in Eastbourne for Camila Giorgi, Madison Keys and Barbora Krejcikova, but Greek third seed Maria Sakkari bowed out, losing 3-6 7-5 6-4 to Ukrainian Anhelina Kalinina.
At the Bad Homburg Open in Germany, the 2019 Wimbledon champion Simona Halep scrambled for a 4-6 6-3 6-4 win against Katerina Siniakova, and sixth seed Amanda Anisimova came from a set down to see off Alison van Uytvanck in a third-set tie-break.
Bianca Andreescu saw off Martina Trevisan 6-3 6-1 and Angelique Kerber also won in straight sets, while top seed and recent French Open semi-finalist Daria Kasatkina reached the quarter-finals with a 6-1 3-6 6-1 win over Germany's Jule Niemeier.
Kasatkina will be absent from Wimbledon due to the ban on Russian players.