Djokovic was below his best in a loss to Australia's Bernard Tomic earlier in the round-robin stage but he demolished Germany's Tommy Haas 6-2 6-0 before Ana Ivanovic defeated Tatjana Malek 6-0 6-1 as Serbia finished top of Group A.
Tsonga's Australian Open preparations were thrown into chaos when he was forced to retire with a groin injury from a mixed doubles match as South Africa beat France 2-1 in a dead rubber in Group B.
Djokovic needed just 62 minutes to beat Haas, hitting 33 winners in his most impressive match of the week.
Djokovic and Ivanovic will meet the Spanish team of Fernando Verdasco and Anabel Medina Garrigues in the final on Saturday.
"I've had a few more hours of sleep," Djokovic told reporters.
"It's great. I came out on court today feeling much fresher than the opening few days. I'm glad I could get a point for Serbia.
"Tommy's a very talented player. He's been struggling with injuries for the last few years.
"He's very persistent to come back into the top ten. I wish him all the best for the Australian Open."
Earlier on Friday, South Africa beat France when Tsonga had to retire in the deciding mixed doubles.
Chanelle Scheepers beat France's Mathilde Johansson 4-6 6-4 6-4 before Tsonga defeated Kevin Anderson 7-6 7-6 during which the French player appeared to slightly injure his groin while stretching for a shot during a rally.
Scheepers and Anderson won the first set of the mixed doubles 6-3 and were trailing 2-1 in the second when Tsonga indicated he could not continue.
Tsonga then announced his withdrawal from the Sydney International, which begins on Sunday. The Australian Open gets underway on Jan. 14. (Writing by Will Swanton, editing by Toby Davis)