A few days after his older sister Nelly won the women's PGA Championship to become the world's top-ranked golfer, Korda maintained a fine family tradition with a superb display.
Striking the ball crisply from the baseline and serving powerfully, Korda kept Evans under control to keep the home fans quiet and claim a relatively comfortable victory.
The world number 50 is coached by his father Petr Korda, a former world number two and 1998 Australian Open champion, and also has former Wimbledon champion Andre Agassi in his team.
Both would have been proud of the way he dispatched Evans after a blip in the second set and then coming back from a break down in the fourth to seize control.
He was the dominant player throughout and struck 51 winners on his way to his second Grand Slam fourth round, having made his breakthrough by doing the same at the 2020 French Open.
For Korda it was his first time on Centre Court and he said it was an occasion he will never forget.
"It was the first time I walked down the stairs, it was incredible," he told reporters. "It was pretty crazy. I almost brought out my phone just to start recording.
"All the years that I've watched tennis, they always show how the players are walking through all the rooms. I just thought to myself, this is nuts.
"What's about to happen is going to be something I'm going to remember for the rest of my life."
If he is to return to Centre Court this year he will have to next get past big-hitting Russian Karen Khachanov, the 25th seed, on Monday.
Evans was one of three British men to reach the third round along with Andy Murray and Cameron Norrie.
It was the first time since 1999 that had happened.
With Murray losing later on, however, hopes now rest on Norrie upsetting eight-time champion Roger Federer on Saturday. Reporting by Martyn Herman, editing by Pritha Sarkar