The world No.1 looked on course for victory when he cruised through the first set of his final Group A match but was outplayed after that in a 3-6, 6-3, 6-3 defeat.
Djokovic ended with one win and two defeats in round-robin play and needs Spain's David Ferrer, who is already guaranteed a place in the semis, to beat Tomas Berdych later at the O2 for him to scramble into the last four.
If Berdych beats Ferrer the Czech would win the group with Ferrer runner-up.
Knowing he required a handsome win to put maximum pressure on Berdych later, Djokovic locked straight into his rhythm from the baseline and broke to lead 3-1 on his way to the opening set.
World number nine Tipsarevic, playing his second match after stepping in for the injured Andy Murray, managed to stay with his Davis Cup teammate in the second set although he was made to work overtime on his service games.
Djokovic, who labeled his poor showing against Ferrer his "worst match" of an incredible season, treated another large crowd to some trademark winners from impossible positions, including one perfect topspin lob.
Tipsarevic, who lost to Berdych on Wednesday despite having a match point, began to strike the ball with more venom and broke for the first time to lead 4-2 when an ambitious Djokovic dropshot attempt landed in the net.
Suddenly a match Djokovic appeared to have firmly under control began to unravel and, although he broke back immediately, Tipsarevic seized on some errors in the next game to regain the advantage and then held serve to set up a deciding set.
Tipsarevic carried his momentum into the third set and broke with an angled winner after dragging Djokovic to the net with a drop shot.
Djokovic never looked like recovering and by the end he looked almost uninterested, ending the contest when he buried a forehand into the net.
Rafael Nadal bowed out of the Tour Finals late Thursday night as the Spaniard had no answer against an inspired opponent, this time in the imposing form of French powerhouse Jo-Wilfried Tsonga.
While Roger Federer's thrashing of Nadal was a masterful demonstration of the sport's classical arts, Tsonga's 6-7, 4-6, 6-3 victory in the final match of Group B was a sustained barrage of heavy artillery that eventually overwhelmed the former world number one.
Tsonga, 26, joined group winner Federer in the semifinals.
Defeat extended Nadal's mediocre record at the season-ender.
In the five years he has qualified he has only made the final once, losing to Federer at the O2 Arena last year.
This year he never looked like adding the prestigious title to his 10 grand slams from the opening day when he labored past tournament debutant Fish in three sets.
"I think I didn't play well tonight," the 25-year-old, who since winning the French Open for a sixth time in June has not won another title, told reporters.
"The first two sets I didn't play bad, but I didn't play well, and to win these kind of matches you have to play well. I played without anything special tonight." While Nadal was clearly disappointed with the level of his performance it would be harsh to take anything away from Tsonga who produced one of the best performances of his career to reach the semi-finals of the event for the first time.
"Tonight, I just played amazing tennis," Tsonga told reporters, adding that he spent the day before the match looking at the video of his run to the Australian Open final in 2008 when he also beat Nadal.
"I was looking at that and I thought, 'Wow!' Before I had lots of energy and I was running faster, hitting harder, but I was crazy on court. This year, maybe I've improved this, but I'm better in my head."
