Czech captain Jaroslav Navratil's decision to go with the experience of veterans Berdych and Stepanek paid off, putting his team in position to get a victory Sunday.
"We played an outstanding match," Berdych said. "It's a shame we lost the second set (but) we'd rather play doubles in a singles way and it has worked so far."
Sunday's deciding reverse singles have Stepanek playing Gilles Simon and Berdych against Jo-Wilfried Tsonga.
The eventual winner faces Argentina in July's quarterfinals.
The Argentines have an insurmountable 3-0 lead over Netherlands.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys