Tomas Holes nodded in the opener 13 minutes after De Ligt saw red for handball following a VAR review, denying Patrik Schick a clear goalscoring opportunity.
Holes then turned provider for Schick as the Czechs doubled their lead on 80 minutes.
The Netherlands, down to 10 men for over half an hour, had a huge chance earlier on as Donyell Malen raced through one-on-one with goalkeeper Tomas Vaclik.
But the Czech Republic went on to silence those in orange at the Puskas Arena in Budapest, setting up a quarter-final with Denmark on Saturday, 3 July.
Source: BBC