Janko Tipsarevic beat Canada's Vasek Pospisil to earn Serbia a 3-2 victory that takes them into the final of the Davis Cup against the Czech Republic.
Novak Djokovic beat Milos Raonic 7-6 (7-1) 6-2 6-2 to pull Serbia level in the semi-final.
Tipsarevic completed the job with a 7-6 (7-3) 6-2 7-6 (8-6) win over Pospisil in Belgrade.
Serbia now face the Czechs, who beat Argentina in their semi-final, in the final on 15-17 November on home soil.
Saturday's doubles win left Serbia trailing but Djokovic pulled the tie level with a straight sets win over Raonic.
After being pushed hard in the first set, Djokovic dominated the remaining two sets to pick up a comfortable victory.
He said: "This is like the [football] World Cup for us."
Tipsarevic faced a much closer contest against Pospisil but after the Canadian saved four match points, the Serb managed to win a second tie-break of the match to take the 2010 winners into a second final in four years.
The Czech team built an unassailable 3-0 lead against Argentina on Saturday.
With Horacio Zeballos beating Lukas Rosol 4-6 7-6 (8-6) 6-4 and Leonardo Mayer defeating Jiri Vesely 6-4 6-4, Argentina cut the final deficit to 3-2 on Sunday.
Spain sealed their return to the World Group against Ukraine on Saturday and Marc Lopez picked beat Denys Molchanov 6-3 6-3 and Fernando Verdasco beat Vladyslav Manafov 6-2 6-1 to wrap up a 5-0 win.