With the tie level at 1-1 after day , Simona Halep got the better of former world number 1 Karolina Pliskova to put Romania 2-1 up.
Katerina Siniakova then beat the decider to be set up by Mihaela Buzarnescu.
And Monica Niculescu and Irina-Camelia Begu conquered Barbora and Siniakova Krejcikova to seal success.
French Open champion Halep, who has vowed to win an initial Fed Cup before she retires, had dug deep to defeat Pliskova 64 5-7 6-4 until Siniakova ran out a comfortable 64 6-2 winner over Buzarnescu.
Krejcikova along with siniakova, the top two players at the doubles rankings and both the Wimbledon champions, were looking to offer the Czech Republic a 12th consecutive home win at the competition, which they’ve won six times as 2011.
They looked on the right track if they took the opening set but Niculescu and Begu broke early in the second group and moved on to level the game.
A group that was nervy saw three breaks of serve in a row at the beginning.
Siniakova and Krejcikova broke back again to make it 4-4 and the momentum appeared to be with them before Begu and Niculescu held their guts for a win.
Additionally to the Semifinals are Belarus and France.
France led 2-0 after Saturday’s play and Caroline Garciaback in the French squad for the first time in two years after having a falling-out with team mates, sealed the win because of a 6-2 6-3 success over Elise Mertens, until Belgium got a point onto the board because of a win in the doubles for Ysaline Bonaventure and Kirsten Flipkens, who beat Pauline Parmentier and Fiona Ferro 10-6 at a third-set tie break.
Aryna Sabalenka and Aliaksandra Sasnovich led Belarus to a 4-0 victory over Germany. While Sabalenka made sure of a semi-final spot with a comfortable success over Laura 24, the set both won day one.
Victoria Azarenka and Lidziya Marozava finished the rout within their game by defeating Mona Barthel and Anna-Lena Groenefeld.