Brunstrom and Lindstedt had other ideas, however, and earned a 3-6, 6-3, 7-6 (7-4), 6-7 (3-7), 10-8 win in four hours and nine minutes to force Sunday's reverse singles to become relevant.
Tipsarevic will get the first chance on Sunday against Michael Ryderstedt, while the second reverse singles match currently calls for Troicki to face Filip Prpic.
Djokovic, along with Serbian captain Bogdan Obradovic, decided that the reigning Australian Open, U.S. Open and Wimbledon champion should rest this week following the No. 1's most recent championship run in Melbourne.
The Serbs defeated the Swedes, 4-1, in the quarterfinals last year.