Six-time champion Roger Federer defeated Kevin Anderson 6-4 6-3 to reach the semi-finals of the ATP Finals for the 15th time.
Federer’s victory means he tops his group to boost his chances of avoiding world number one Novak Djokovic in the last four in London.
The Swiss, 37, looked out of touch when he lost his first match on Sunday but hit back with two successive wins.
South African Anderson had already won two matches to reach the semi-finals and was full of confidence heading into his toughest test.
Top seed Djokovic has already secured his spot in the semi-finals and can clinch top spot in his group by beating Marin Cilic on Friday.
Alexander Zverev, John Isner and Cilic are battling for the other semi-final berth.
Questions were asked about Federer’s form and state of mind after he lost to Kei Nishikori in straight sets on Sunday but he gave himself a chance of reaching the semi-finals by beating Dominic Thiem on Tuesday.
“I’m very happy, my first match was tough and I never got going, but with my back against the wall maybe it’s easier for me to play,” said Federer.
“Kevin’s had a great year, but it’s been a fun group and I’m very happy to be in the semis.”
“These round-robin formats are not straightforward, we’re used to it being you lose, you leave, you don’t hang around,” added Federer.
“Maybe it was difficult for Kevin having already qualified, whereas with Thiem winning it was maybe easier for me.
“But I’m happy I’m still alive and hope I can play a good match the day after tomorrow.”
