World number eight Tipsarevic needed two hours and 26 minutes to see off Kohlschreiber 6-4 3-6 7-5, giving Serbia an unassailable 2-0 lead after Viktor Troicki's win over Florian Mayer on Thursday.
Germany grabbed a degree of consolation in the Blue Group tie when Philipp Petzschner and Christopher Kas teamed up to defeat Miki Jankovic and Nenad Zimonjic 6-4 6-4 in the doubles rubber.
Serbia will face the Czech Republic in the final after Frantisek Cermak and Radek Stepanek kept their nerve to clinch the deciding doubles rubber over Argentina's Carlos Berlocq and Leonardo Mayer.
The Czech pair triumphed 6-4 4-6 10-3 to take the tie after Mayer had earlier given the Argentinians hope by beating Stepanek 7-6 (7/4) 5-7 6-4 in their rubber, hauling the tie back to 1-1.
In remaining action, Igor Kunitsyn and Dmitry Tursunov teamed up to beat Ivan Dodig and Lovko Zovko 2-6 6-4 10-3 and give Russia a 2-1 win over Croatia. Earlier, Alex Bogmolov had hauled Russia level by beating Zovko 6-4 6-2 in their singles rubber.