With the best-of-five series tied 1-1 entering Sunday, Cepelova -- substituting for the injured Dominika Cibulkova -- gave Slovakia the advantage by rallying over Serbia's Bojana Jovanovski 5-7, 7-5, 11-9.
Hantuchova then clinched Slovakia's victory with a convincing 6-3, 6-2 rout of Vesna Dolonc.
Serbia closed out the test with dead-rubber doubles triumph, making the final margin 3-2.
The decision put Slovakia into an April semifinal against Russia, advanced over Japan this weekend with a 3-2 quarterfinal victory.
Notable deaths of 2014 [PHOTOS]