Muchova won 4-6 7-5 13-11 in three hours 17 minutes, claiming victory with a netcord as former world number one Pliskova's wait for a first Grand Slam title continued.
In her first Grand Slam quarter-final world number 68 Muchova will face eighth-seeded Ukrainian Elina Svitolina after she eased past Croatia's Petra Martic.
Had Pliskova not dropped serve in the final game of a high-quality duel, Wimbledon would have witnessed its first final set tiebreak at 12-12 -- the new rule brought in after last year's tournament to prevent 'never-ending' final sets.
With Australian world number one Ash Barty's defeat in the earlier fourth-round tie on Court 2, Pliskova began the match as the highest seed left in the women's draw and with a golden chance to reach the quarter-finals here for the first time.
The big-server seemed on course when she took the opener against her 22-year-old compatriot.
But Muchova, making her main draw debut this year, was undaunted and took the match to her more illustrious opponent with some sparkling tennis.
Pliskova squandered a 5-3 lead in the final set and then served for the match again at 11-10 but was broken to love.
The tenacious Muchova did well to hold serve at 11-11 before going 0-40 up on the Pliskova serve thanks to a stunning clean winner off a forehand service return.
Pliskova got back to 30-40 with her opponent slipping over on her second match point but Muchova got lucky at the third attempt as her forehand return clipped the tape and dropped dead.