Leicester’s Boulter dropped the first set to Pliskova 6-3 but bounced back to take the next two sets 7-6, 6-4.
Fellow Britons Liam Broady and Heather Watson also earned memorable wins on Thursday to reach the third round.
Wildcard Broady defeated the 12th seed Argentinian Diego Schwartzman 6-2, 4-6, 0-6, 7-6, 6-1 to record his best ever performance at a major.
British number four Watson matched her best Wimbledon singles performance with a 7-5, 6-4 win against China’s Wang Qiang.
There was disappointment for Harriet Dart who won the opening set against eighth seed Jessica Pegula, only for the American to fight back to win 4-6, 6-3, 6-1.
Briton’s Jack Draper failed to make it into the next round after suffering a four-set defeat against Australian 19th seed Alex de Minaur.
British wildcard Alastair Gray ranked 288th and making his men’s singles debut at Wimbledon, fell to American 11th seed Taylor Fritz in straight sets.
No problems for the women’s number one seed Iga Swiatek. Despite dropping a set, she booked her place in the next round with a 6-4,4-6 6-3 victory over Lesley Pattinama Kerkhove.
In the men’s event the number two seed Rafa Nadal defeated Lithuanian Ricardas Berankis in four sets.
Unseeded wild boy Nick Kyrgios brushed aside the number 26 seed Filip Krajinovic in an hour and a half with a comfortable straight sets victory.
French girl Harmony Tan who knocked out Serena Williams this week had another fine victory when she got the better of Spaniard Sara Sorribes Tormo in straight sets 6-3, 6-4.
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