(Recasts after second semi-final)
By Martyn Herman
LONDON, Nov 21 (Reuters) - Rafa Nadal's dream of a first ATP Finals title and Novak Djokovic's quest for a record-equalling sixth vanished in defeats by Daniil Medvedev and Dominic Thiem in two seismic semi-finals on Saturday.
As the curtain comes down on London's 12 years as host of the ATP Tour's prestigious season-ender, it would have been fitting for Nadal and Djokovic to face off for the 57th time in their glittering careers.
But times are a changing, or so it seems, and Medvedev and Thiem had not read the script.
Nadal, seeking the one major pot missing from his vast collection of silverware, must have seen the door creaking open when Thiem produced a staggering fightback to beat Djokovic 7-5 6-7(10) 7-6(5) in a classic contest lasting almost three hours.
He had beaten Medvedev in each of their three meetings, including a memorable U.S. Open final last year.
It seemed like he had exhausted the wily Russian's box of tricks when he served for the match at 5-4 in the second set but Medvedev, 10 years his junior at 24, stormed back to win 3-6 7-6(4) 6-3.
Whatever happens on Sunday it will mean a fifth consecutive first-time winner of the tournament.
"At 5-4 in the second set I decided to change some small things and start going for things a little more. I had to change and it worked really well," said Medvedev, who was 100% in group play, including a win over Djokovic.
To put world number four Medvedev's win into perspective, Nadal had triumphed in the last 71 matches in which he had taken the first set.
Medvedev looked the more likely winner as he raced through his service games in the opening set while Nadal laboured.
But the Spaniard pounced as Medvedev suffered a momentary dip at 3-4 and suddenly he was a set to the good.
Undeterred, Medvedev kept hammering away and Nadal dipped at the start of the second set, dropping serve with a double fault. Medvedev squandered a point for a 5-1 lead and paid the price as Nadal hurtled back to stand on the brink of victory.
Medvedev broke to love, though, and the set moved into a tiebreaker. A flukey forehand winner helped Medvedev into a 5-3 lead and he stayed composed to take it.
Nadal slowed under the relentless barrage in the third, but it was still a surprise to see him fade at the end, losing the last three games as Medvedev romped home.
Earlier in the empty arena, the 27-year-old Thiem saw four match points vanish in the second set tiebreak against Djokovic, one with a nervy double-fault, and it seemed he would pay a heavy price.
Djokovic, who is one short of Roger Federer's titles record at the ATP Finals, led 4-0 in the deciding set tiebreak.
But U.S. Open champion Thiem unleashed a stunning counter-attack to reel off six points, reaching match point with a ripping crosscourt backhand.
Djokovic saved a fifth match point but then floated a defensive forehand long.
"What he did from 0-4 in the tiebreak was unreal," Djokovic, who won the title in London from 2012-15, told reporters. "He just crashed the ball and everything went in. What can you do?"
Thiem, who racked up his 300th career Tour win, is now established as a major force and will attempt to go one better than last year when he lost to Stefanos Tsitsipas in the final.
"From 0-4 in the third-set tiebreak I went for every single shot and every single shot went in. It was amazing," he said. (Reporting by Martyn Herman; editing by Clare Fallon and Ed Osmond)