Thiem ends Djokovic's ATP Finals record bid in London thriller
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The Austrian third seed's 7-5, 6-7 (10/12), 7-6 (7/5) win ended Djokovic's hopes of equalling Roger Federer's record of six titles at the elite eight-man event.
The US Open champion will face either Rafael Nadal or Daniil Medvedev in Sunday's final at London's O2 Arena as he chases the second-biggest title of his career.
The 2019 runner-up, who forced the only break of the match in the first set, faced an uphill battle psychologically after his missed chances in the second-set tie-break.
But he was quickly back in the groove and rallied from 4-0 down in the final-set tie-break, winning six successive points to earn two match points, taking the second of those.
"It was for sure a mental battle," said Thiem. "I got so tight in the second-set tie-break, first of all because to play these legends is always going to be something special.
"And then playing for a final here at the ATP Finals is also something very special. I thought after my first big title in New York, maybe I'm going to be a little bit more calm but that was a mistake I guess.
"I was just as tight and nervous as before and it was so much on the edge... I'm incredibly happy to be through."
Thiem took time to settle at the start of the contest, hitting a number of unforced errors, but found his rhythm and his single-handed backhand became an dangerous weapon as the match wore on.
The third seed produced a searing forehand winner to set up break point in the 11th game of the first set and Djokovic netted with a volley.
The 27-year-old closed out the set impressively, lashing a backhand winner down the line before producing an ace.
Djokovic, 33, earned his first break point of the match in the eighth game of the second set and had two more in the 12th game but each time Thiem snuffed out the danger.
In a nailbiting tie-break, Thiem squandered four match points and eventually dumped a backhand into the net as the 17-time Grand Slam champion took it 12-10 to level the match.
Both players settled quickly at the start of the decider, with Djokovic looking far more focused than he had in the latter stages of the second set.
There were no break points in the third set and both players braced for another tie-break.
Thiem looked down and out at 4-0 down in the shootout but rallied impressively, converting his sixth match point with a powerful forehand approach shot.
The Austrian is only the second player in 2020 to win a tie-break against Djokovic, who entered the third-set decider with a 15-1 tie-break record this season.
Djokovic, who has already tied Pete Sampras's record mark of six year-end number-one finishes, has not won the season-ending championships since 2015.
"What he did from 0-4 in the third-set tiebreaker was just unreal," said the world number one. "I mean, I don't think I played bad."
"He just crushed the ball," he added. "Everything went in from both corners, and he played a couple of very short slices, you know, angles. Yeah, I mean, what can you do?"
Thiem has lifted himself into the top echelon of the men's game, reaching the Australian Open final this year, where he lost to Djokovic, before his triumph at Flushing Meadows in September.