Dominic Thiem became the first man to move into the last four of the ATP Finals event in London.
The Austrian beat Rafael Nadal 7-6 (9-7) 7-6 (7-4) in a high-quality match for his second victory of the season-ending event at the O2 Arena in London.
Nadal had two set points in the first-set tie-break but could not convert with Thiem eventually securing the win on his fifth match point.
Thiem's qualification was secured when Stefanos Tsitsipas beat Andrey Rublev.
Defending champion Tsitsipas survived a match point as he won 6-1 4-6 7-6 (8-6) in Tuesday's other match of Group London 2020.
Tsitsipas will play Nadal on Thursday with the winner joining Thiem in the semi-finals, while Rublev is eliminated after two defeats from two.
"It was a great match from the first to last point," said Thiem of his win over 20-time Grand Slam winner Nadal. "I was pretty lucky to get that first set after being 5-2 down in the tie-break.
"I had the feeling that the match was a very high level. The atmosphere would've been unreal [if fans were in the arena]. We put on a good show for those watching on television."
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Thiem prevails in two gripping sets
Spanish second seed Nadal, who is seeking his first ATP Finals title, and Thiem have brought the best out of each other on many occasions in recent years, with gripping matches at the Australian and US Opens, plus two French Open finals. They did so again here over two hours and 25 minutes when the superb standard barely dropped.
It was such a shame that there was no crowd to enjoy the dazzling shot-making in a first set that went to a tie-break without a break point being created.
Nadal seemed set to take it when he led 5-2 and although Thiem clawed his way back to 5-5, a double fault handed the 34-year-old Spaniard a set point. An uncharacteristic backhand into the middle of the net allowed the Austrian to escape and after Thiem saved another set point, he took his own first opportunity with an inside-out forehand winner.
The first break of the match went Nadal's way in the seventh game of the second set but 27-year-old Thiem hit back straight away to level at 4-4, before holding serve to put the pressure on the 20-time Grand Slam champion.
Nadal faltered as three errors gave the US Open champion three match points at 0-40 but the Spaniard won the next five points to hold, including a serve-volley at 15-40 that clipped the tape and dropped on his opponent's side.
The set went into another tie-break and at 3-3, a magnificent backhand winner saw Thiem seize the initiative with the victory secured when Nadal dragged a backhand wide.
It was Thiem's seventh win in nine matches against top 10 players this year.
"I think that today I played a little bit higher level than at the US Open. It was maybe the best match from me since the restart of the tour and that makes me super happy," he added.
Nadal, who beat Rublev in straight sets in his opening match on Sunday, said the way he played against Thiem makes him feel confident for the rest of the tournament.
"It has been a great match of tennis decided for a few small details," he said. "Just well done to him. He played, I think, an amazing match and I played well too.
"My feeling is not negative. I lost but I had plenty of chances in the first and then I had a break in the second. I think my chances are bigger to have a very good result now than five days ago because the level of tennis, even if I lost today, is much higher."
Tsitsipas sets up Nadal eliminator
Tsitsipas, 22, looked on course for a routine win over Rublev when he took the opening set in only 19 minutes.
However, the 23-year-old Russian broke late on in the second to take the match into a decider.
Rublev led 6-5 in the final-set tie-break but served a double fault, only his second of the match, as Tsitsipas won three points in a row to set up an effective knockout match against Nadal.
"It was an unbelievable match from both sides and we produced some incredible tennis," Tsitsipas said.
"Putting in all that fight paid off and I'm happy I showed the determination and willingness not to give up when he had match point. I produced some good tennis and that helped me take the win."
Rublev's defeat means his match against Thiem on Thursday is a dead rubber.
How they stand
|Group London 2020|
|Matches won-lost||Sets won-lost||Games won-lost|
|1. Dominic Thiem||2-0||4-1||31-27|
|2. Rafael Nadal||1-1||2-2||24-21|
|3. Stefanos Tsitsipas||1-1||3-3||32-30|
|4. Andrey Rublev||0-2||1-4||20-29|
What's happening on Wednesday?
Germany's Alexander Zverev plays Argentine Diego Schwartzman in Group Tokyo 1970 with both players seeking their first win of the event in a match you can watch on BBC Two and the BBC Sport website and app from 14:00 GMT.
World number one Novak Djokovic and Russian Daniil Medvedev - who both won their openers in straight sets - play in the evening session (20:00 GMT), with live commentary on BBC Radio 5 Live Sports Extra, plus the website and app.
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