In Group A play, Tipsarevic rallied for a 3-6, 6-3, 6-3 win to send Djokovic to a second loss in round-robin action. The world No. 1 also fell to David Ferrer on Wednesday and didn't gain a semifinal berth after Berdych rallied past Ferrer on Friday, 3-6, 7-5, 6-1.
Ferrer has already booked his spot in Saturday's semifinals, and will face Roger Federer in the first match. Federer reached the semifinals from Group B along with Jo-Wilfried Tsonga, who will face Berdych in Saturday's second match.
Federer, who went unbeaten in Group B, is gunning for a record sixth title at the season-ending event.
Tsonga beat Rafael Nadal on Thursday to earn his berth. Nadal, ranked second in the world, was the runner-up to Federer at this event last year.
Tipsarevic, who replaced an injured Andy Murray earlier this week, finished at 1-1 in round robin play. Murray lost to Ferrer on Monday, then withdrew because of a groin injury. Tipsarevic was the first alternate and lost to Berdych on Wednesday.
Djokovic, the 2008 champion of this event, dropped just four points on serve in the opening set, then had plenty of chances to break serve in the first game of the second set. Tipsarevic, though, survived the 18-point first game and broke serve for a 4-2 lead. He failed to hold in the next game, but again broke Djokovic for 5-3 before holding to force a decisive set.
A break of serve in the opening game of the third gave Tipsarevic the edge and he never relinquished it. He broke serve again, after Djokovic saved two match points, to finish the two-hour, eight-minute match.
Berdych secured his place thanks to strong final set, when he raced off to a 5-0 lead. He finished with seven aces and won 83 percent of his first-serve points, while getting his first serve in play 45 percent of the time.