After finishing Saturday tied at 1-1, Slovakia broke away from Serbia on Sunday, winning both singles matches to go up 3-1 and reach the semifinals for the first time since winning the title in 2002.
The first match of Day 2 could have gone either way as Jana Cepelova took on Bojana Jovanovski, the two players battling it out for three hours and 18 minutes - but in the end it was Cepelova who squeaked it out, rallying from 2-0 and 4-2 deficits in the third set and eventually prevailing, 57 75 119.
"We all came here to do our best," Hantuchova said. "In Fed Cup you don't just come here to play for yourself, you come here to play for your country, and I think that's why we all made the effort to come here even though the scheduling is difficult. We're just all very proud to play for our country.
"When we won the Fed Cup in 2002 it was one of the most incredible emotions I've ever felt on the tennis court. To be able to do it again would be something unbelievable. We've got a fantastic team and we're all very motivated right now, and if we just take it step by step, I think we have a chance."
Slovakia had to give a walkover in the doubles match and thus ended up with a 3-2 victory.
Awaiting Slovakia in the semifinals will be Russia, who scored a 3-2 win against Japan. The two teams were tied 1-1 after Saturday and it was still even at 2-2 after Sunday's singles matches - Ayumi Morita beat Elena Vesnina, 64 61, then Ekaterina Makarova defeated Kimiko Date-Krumm, 61 61.
It all came down to the doubles match and while they had mixed results in the singles, Makarova and Vesnina - one of the best doubles teams in the world - rose up, beating Morita and Misaki Doi, 62 62.
"It was tough but amazing days for us - we're so happy we were able to beat Japan and make the semifinals again," Vesnina said. "Ekaterina was a hero today, she won such an important point for our country in the singles then played so well in the doubles, so I'm really proud of her for that."
"I made some mistakes the day before but worked on those and I'm very happy I could help bring these points to my team," Makarova said. "I was expecting the Japanese to be tough this weekend because they're great players - if they made it to the final eight of Fed Cup, they had to be playing great."
Makarova and Vesnina won a pair of Premier-level doubles titles together last fall - Beijing and Moscow - and are both in the doubles Top 10. Vesnina talked about how that helped them this weekend.
"We've played quite a long time together and have some special things we do in key moments, and we were very happy those things worked against Morita and Doi today," Vesnina said. "We were just trying to play our game and thank God everything worked today like we were planning. It was a good day."