Britain's Boulter dedicates Pliskova win at Wimbledon to late grandmother
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Boulter, 25, came from a set down to beat the Czech sixth seed 3-6, 7-6 (7/4), 6-4 on Centre Court, to the delight of the home fans.
"I have absolutely no words right now," said the emotional world number 118. "I am literally shaking. The crowd was unbelievable so thank you for getting me through that.
"I'm probably going to getting emotional. My grandmother died two days ago so I'd like to dedicate that to her today.
"It's a dream come true for me and if I can have you behind me I can probably go a long way."
Pliskova broke twice in the opening set to establish a firm grip on the match but Boulter won the second-set tie-break to level.
A single break in the decider was enough for the British player, who hit 25 winners, to seal the match.
She will next face Serena Williams's conqueror Harmony Tan after the French player beat Spain's Sara Sorribes Tormo, seeded 32, 6-3, 6-4.