It was Kontaveit's first win in four meetings with Pliskova.
Denmark beat the Czech Republic 2-1 in a nervy European Championship quarterfinal to reach the semifinals of the competition for the first time since they won the title in 1992.
De Boer has resigned two days after his side were beaten 2-0 by the Czech Republic and eliminated in the last 16 of the European Championship.
The loss of De Ligt was immediately felt as the Dutch went from being comfortably in control to being forced onto the back foot by a muscular Czech side.
Striker Patrik Schick scored his fourth goal of the tournament as the Czech Republic upset 10-man Netherlands with a deserved 2-0 victory.
England delivered an efficient but hardly scintillating display to beat the Czech Republic 1-0 with an early Raheem Sterling header.
Perisic scored a stunning second half equaliser as Croatia pegged back the Czech Republic for a 1-1 draw in Group D, keeping their slim hopes alive of qualifying to the knockout stages.
Schick put the Czechs in front three minutes before half-time as he towered above two defenders to power home a header, but his second goal seven minutes into the second half will almost certainly be one of the tournament’s greatest.
Fourth seed Sofia Kenin claimed her maiden French Open semifinal spot as she fought to a 6-4, 4-6, 6-0 victory over fellow American Danielle Collins.
The WTA also announced a revised system for calculating world rankings when the season resumes.