Serbia, the 2010 champions, will host the November 15-17 final against the Czechs who had already made sure of victory in their semi-final on Saturday when they opened up an unassailable 3-0 lead against Argentina in Prague.
World number one Djokovic kept Serbia alive in Belgrade yesterday by seeing off world number 11 Milos Raonic 7-6 (7/1) 6-2 6-2.
Tipsarevic, the world number 24, then assured Serbia of a second final in four years by defeating Vasek Pospisil 7-6 (7/3) 6-2 7-6 (8/6).
"I played at my own tempo from the beginning and I knew the returns would be crucial, so I paid special attention to them," said Djokovic, who had defeated Pospisil in Friday's opening singles.
In Prague, Argentina won the two dead rubbers with Horacio Zeballos beating Lukas Rosol 4-6 7-6 (8/6) 6-4 and Leonardo Mayer defeating Jiri Vesely 6-4 6-4.
Radek Stepanek and Tomas Berdych, who had won their singles on Friday, had wrapped up the tie for the Czech Republic on Saturday by beating Carlos Berlocq and Zeballos in the doubles, 6-3 6-4 6-2.
The victory gave Pat Rafter's team an unassailable 3-1 lead.
Tomic won his second singles rubber of the tie after he and Lleyton Hewitt gave Australia a 2-0 lead on the opening day.
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