Dlouhy's 1-6, 7-6 (7-3), 7-5 victory over Christopher Rochus came after Belgian Steve Darcis gave the home team its only point of the weekend with a 7-6 (8-6), 1-6, 6-4 win over Jan Hajek.
Tomas Berdych and Radek Stepanek, with singles wins Friday and a doubles victory Saturday, had already assured the Czech Republic of advancing to July's Davis cup quarterfinals. The Czechs will go against either Chile or Israel in that round.
Berdych and Stepanek didn't allow the Belgians to win a set in the first three matches of the series.
Hajek's win in the first-set tie-break got the Belgians their first set and he hung on in the third set to get the point.
Dlouhy rallied after a first set in which he won only 17 points to even the match with a tie-breaker and served out after an 11th-game service break.
Notable deaths of 2014 [PHOTOS]