Serbia, without Novak Djokovic, proved no match for Slovakia who surged into the Davis Cup group stage finals for the first time on Saturday, with Germany and Finland also booking their berths.
Slovak doubles duo Lukas Klein and Igor Zelenay clinched the decisive point with a 7-6 (7/4), 6-3 win over Nikola Caci and Miomir Kecmanovic to take an unassailable 3-0 lead in the tie.
Lukas Pokorny made it 4-0 after Laslo Djere retired while trailing in the first set of the reverse singles on indoor clay at Kraljevo.
"Too many years we didn't qualify but finally we made it," said Zelenay.
Alex Molcan, who won Friday's second singles, added: "We knew it was going to be tough against Serbians in their home nation. I'm happy we were able to win two matches today."
Zelenay and Klein had recovered from a break in the first set, digging deep with 31 winners to see off 2010 champions Serbia.
On Friday, Klein got Slovakia off the mark with a 7-6 (7/2), 6-2 win over Kecmanovic, with Molcan rallying past Dusan Lajovic 4-6, 6-2, 6-0.
In Hungary, three-time winners Germany -- missing Alexander Zverev due to illness -- clinched both of Saturday's matches for a 3-1 victory.
Doubles pairing Kevin Krawietz and Tim Puetz's 6-3, 7-6 (7/3) win over Fabian Marozsan and Mate Valkusz pulled the Germans ahead.
Jan-Lennard Struff sealed their ticket with a 6-3, 6-2 win over Valkusz to advance to September's group stage finals featuring 16 teams.
On Friday, the United States advanced 4-0 with Austin Krajicek and Rajeev Ram sealing their spot with a doubles win against Ukraine.
Taylor Fritz then eased past Vladyslav Orlov 6-3, 6-4 to complete an American sweep.
"I'm proud of the guys," said US captain Bob Bryan of the record 32-time winners who have not lifted the trophy since 2007.