Nadal, playing his first match since losing to Roger Federer in the Wimbledon semi-finals, fell behind 5-2 in the tiebreak before roaring back to prevail in his first career meeting with world number 53 Evans.
It was Kristyna's first win over a top-five ranked player and she will go on to play fellow Czech Barbora Strycova in the quarter-finals.
Rafael Nadal will skip the Miami Open that begins later this month in a bid to recover from a back injury in time for the clay court swing
IMAGES from Day 1 of all the action from the Wimbledon Championships played at the All England Lawn Tennis and Croquet Club, London, on Monday.
Images from the matches played at the All England Lawn Tennis and Croquet Club, in Wimbledon, London, on Monday.
IMAGES from the matches played at the PNB Paribas Open at Indian Wells on Sunday
The 32-year-old, five-times a winner of the singles at the prestigious Wimbledon warm-up event, delighted a large evening centre court crowd with some fluent shot-making as he and Spanish veteran Lopez beat top seeds Juan Sebastian Cabal and Robert Farah 7-6(5), 6-3.
Images from Day 7 of the 2020 US Open in New York on Sunday.
Images from Day 4 of the Wimbledon tennis championships played in London, on Wednesday.
Thursday's match was just Venus Williams's seventh of the year and first since January's Australian Open, where she fell to Simona Halep in the round of 32.
The Scot lost 6-4, 6-4 to Richard Gasquet in his first singles match since January before saying he had turned down a wild card into the men's draw at the year's final Grand Slam.
Images from Day 7 of the 2021 Wimbledon at the All England Lawn Tennis and Croquet Club, in London, on Monday.
A summary of Friday's play at Wimbledon.
Images from Day 2 of the 2020 US Open in New York