Novak Djokovic moved past Alexander Zverev in straight sets to reach the last four of the ATP Finals.
The Serb world number one beat German Zverev 6-3 7-6 (7-4) at the O2 Arena in London.
Djokovic, seeking a record-equalling sixth title at the end-of-season tournament, was pushed much more in the second set but raised his level at the crucial time in the tie-break.
He will play Dominic Thiem in the last four on Saturday at 14:00 GMT.
That match is live on BBC One and the BBC Sport website.
US Open champion Thiem progressed as winner of Group London 2020 with Djokovic going through in second position in Group Tokyo 1970.
The other semi-final is between Rafael Nadal and Daniil Medvedev, who first plays a dead rubber against Diego Schwartzman at 20:00 GMT on Friday.
“I felt great. In the first set he had a couple of break-point chances and I managed to serve well in the important moments,” said 33-year-old Djokovic.
“In contrast to the match against Daniil, I found the right shots at the right time. I have tremendous respect for Sascha, who is a great player and it is not easy to return 140mph first serves.
“It was anybody’s game for most of the match.”
Djokovic quells Zverev fightback in second set
Their five previous meetings had all been won in straight sets without any of them going to a tie-break and it seemed as though this match would follow the pattern as Djokovic, who was victorious in three of them, dominated the early stages.
He was into the groove with a love hold, while Zverev gave up his first service game in predictable fashion, conceding the break with a double fault.
Zverev did bring up two break-back points at 2-4 but first serves and clean hitting from the baseline helped Djokovic see them off with little fuss, before the Serb sealed the set with a trademark backhand down the line.
The second set was much more competitive with Zverev twice shouting “come on” when saving two break points at 2-2. As ever, though, the differential between his first and second serves was key to the match, with the 2018 champion winning 83% of points on his first delivery and only 35% on his second.
Zverev twice came within two points of the set when Djokovic was serving but the 17-time Grand Slam champion remained solid at key moments, as they eventually played their first tie-break together.
The 23-year-old moved to a 2-0 lead but Djokovic quickly levelled and then got the decisive mini-break with a backhand cross-court winner for 5-3.
“Novak served incredibly well, I thought,” said Zverev. “I had to go very far back to return his serve. It was very difficult for me.
“I started playing really well in the second set, so a few points decided the set.”
Looking ahead to his semi-final against Austrian Thiem, Djokovic added: “Obviously earlier in his career Dominic played his best on clay but being one of the hardest workers on tour, and most dedicated players, found his A-game on other surfaces, and his first Slam came on a hard court earlier this year in New York.
“I played him here last year and lost 7-6 in the third set, it was a thrilling match. Hopefully have another great match – with a different outcome.”