It was the second World Team Cup title for the Serbs, who swept the Czech Republic in the two singles matches as well as doubles play.
Tipsarevic knocked off Tomas Berdych 7-5, 7-6 (10-8) and Troicki followed with a 2-6, 6-4, 6-3 win over Radel Stepanek. Tipsarevic and Nenad Zimonjic went on to win the doubles contest 6-3, 6-1.
Both Serbia and the Czechs went 3-0 in group play leading up to Saturday's finals.
Celebrity Families of 2014 [PHOTOS]