The 25-year-old went into the match full of confidence after a fine run of tournaments on the grass, including victory over Pliskova in Eastbourne last week.
And, after defeats for Emma Raducanu and Andy Murray on Centre Court on Wednesday, Boulter thrilled the home crowd by coming from a set down to win 3-6 7-6 (4) 6-4.
Boulter then became emotional during her post-match interview as she dedicated the victory to her grandmother, who died two days ago.
“It’s been a tough few days for sure,” she said. “I’ve tried to kind of get my emotions out and deal with the situation, try and keep my head on the tennis. Her favourite tournament was Wimbledon. That’s why it’s a special one for me. She’d watch every single match that was on the TV.”
Boulter next takes on France’s Harmony Tan, who followed up her victory over Serena Williams by defeating Sara Sorribes Tormo.
Boulter was joined in the last 32 by Heather Watson, who needed just one game to complete a 7-5 6-4 win over Wang Qiang in a match held over from Wednesday night, and a delighted Liam Broady.
Broady faced a rematch against 12th seed Diego Schwartzman, who he lost to in four sets last year, and he turned the tables by coming from two sets to one down to win 6-2 4-6 0-6 7-6 (6) 6-1.
Boulter and Broady are two of the players with most cause to rue the ATP and WTA’s decision to strip Wimbledon of ranking points in response to the ban on Russian and Belarusian players.
“I’m losing 45 points from last year, so I think I’ll probably drop back now to 150,” said Broady, who is yet to crack the top 100.
“But I’m just grateful to have made the third round of Wimbledon, to be honest. I’d play Wimbledon for no points and no prize money.”
Watson has been resurgent this week, reaching the third round at a slam for the first time in five years, and with the chance to finally make it further when she meets Kaja Juvan on Friday.
“I’m pretty relaxed about it right now,” said Watson. “I’ve been here before. I’m just taking it step by step, match by match.
“I feel, as I’ve gotten older, I’ve been on the tour many years now, my highs aren’t as high, but my lows aren’t as low.”
Broady will take on 19th seed Alex De Minaur, who won a fierce four-set battle on Court One against 20-year-old British player Jack Draper to join girlfriend Boulter in the third round.
Draper won the first set but ultimately was unable to match the physicality of De Minaur in a 5-7 7-6 (0) 6-2 6-3 defeat.
Harriet Dart also claimed the first set against eighth seed Jessica Pegula but lost out 4-6 6-3 6-1 while debutant Alastair Gray was beaten 6-3 7-6 (3) 6-3 by 11th seed Taylor Fritz.