Minar raced by Nicolas Massu 6-0, 6-2, 6-3 and Hajek routed Paul Capdeville 6-0, 6-2, 6-1.
Those wins put the Czech Republic one win from qualifying for September's Davis Cup semifinals against either Croatia or Serbia, which split their two matches Friday.
Capdeville and Jorge Aguilar must win Saturday's doubles match for Chile over Czechs Frantisek Cermak and Lukas Dlouhy to have Sunday's singles mean anything. Massu is to play Hajek and Capdeville goes against Minar in the final two singles matches.
Hajek won 62.5 percent of the points against Capdeville, including 60 percent off Capdeville's serve. Minar took 62 percent of points in his match and Massu didn't force one break-point opportunity.