Muchova, 29, used her athletic game of precise volleys, delicate drop-shots and searing cross-court winners to overcome Krejcikova, at 30 just eight months older than Muchova, and now ranked 38th in the world.
Muchova declared herself very relieved to be the one undertaking the winner's courtside interview in warm sunshine on Court Two. The players grew up together as juniors and know each other's games well.
"She's not a Wimbledon champion by chance," Muchova said of her opponent.
"She deserved that second set. I'm just glad I'm making the interview here with you."
After a cagey start, Muchova stepped up her aggression in the 12th game, attacking the Krejcikova serve and winning the first set with a sizzling cross-court backhand return. She produced a total of 50 winners in the match, to Krejcikova's 24.
She wore down her compatriot in a mammoth 16-minute sixth game of the second set, taking it on her fourth break point.
But just when she looked down and out, Krejcikova, who also has the 2021 French Open title to her name, roared back to win five games in a row and force a decider.
Muchova steadied her nerves and grabbed a break in the fourth game of the third set as Krejcikova, whose career has been beset by injury, appeared to tire in the heat. Muchova took the match with a lobbed forehand winner before hugging her opponent at the net.
Muchova, who has now equalled her best Wimbledon showing by reaching the last eight, has won two titles this year, at Bad Homburg last month and at Doha. She said she was really enjoying her tennis.
"I'm incredibly happy for the whole season," she said. "It's nice to have some wins which give confidence."