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 now needs the Spaniard to beat Tomas Berdych later Friday to qualify for the final four.
Ferrer has already booked his spot in Saturday's semifinals.
Roger Federer and Jo-Wilfried Tsonga reached the semifinals from Group B, with Tsonga beating 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.
Federer, who went unbeaten in Group B, is gunning for a record sixth title at the season-ending event.