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 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).
But Pospisil went down fighting, coming back from 5-2 down in the third set and saving four match points in the ensuing tiebreaker.
"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.
Australia returned to the World Group for the first time in six years with Bernard Tomic supplying the crucial third point against Poland with a 6-4, 7-6 (7/5), 6-3 win over Lukasz Kubot in Warsaw.
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.
Poland kept the tie alive as Marcin Matkowski and Mariusz Fyrstenberg defeated teenage debutant Nick Kyrgios and Chris Guccione in Saturday's doubles.
The victory means Australia, 28-time Davis Cup champions, will return to the top 16 for the first time since 2007.
The tie finished 4-1 when Michal Przysiezny retired when 4-1 down in the first set against Kyrgios.
Andy Murray secured Britain's return to the World Group after a five-year absence when he defeated Croatia's Ivan Dodig 6-4, 6-2, 6-4 in Umag for a 3-1 advantage.
Wimbledon and Olympic champion Murray won his opening singles on Friday and teamed up with Colin Fleming to win the doubles on Saturday.
"I thought it was pretty good match. I didn't give him a lot of opportunities on my serve," said the world number three.
For Croatia, the defeat means that they fall out of the World Group for the first time since 2008, having won the trophy in 2005.
World number 12 Kei Nishikori helped propel Japan back into the World Group with a 3-2 comeback victory over Colombia in Tokyo.
Nishikori overpowered Santiago Giraldo 6-1, 6-2, 6-4 to level the tie before Go Soeda held his nerve to beat Alejandro Falla 4-6, 6-4, 6-3, 6-3.
Daniel Brands maintained Germany's World Group status by sealing a 3-1 victory over Brazil after stepping in as a late replacement after illness to Philipp Kohlschreiber.
Brands, 26, who made his Davis Cup debut in Saturday's doubles, enjoyed a 6-4, 6-2, 6-3 win over Thomaz Bellucci.
In Antwerp, Steve Darcis, the man who knocked Rafael Nadal out of Wimbledon, defeated Amir Weintraub 6-2, 6-2, 6-2 as Belgium secured a World Group place at the expense of Israel.
Ruben Bemelmans had earlier put Belgium back on level terms at 2-2 by beating Israeli number one Dudi Sela 7-5, 3-6, 6-0, 6-4.
Spain, the Netherlands and Switzerland had already tied up victories on Saturday over Ukraine, Austria and Ecuador respectively.