- Federer finishes second in Group Bjorn Borg, behind Thiem, who also beat Djokovic earlier this week. The Swiss will face the Group Andre Agassi winner on Saturday.
- Djokovic looked nervy at the start of the winner-takes-all contest, double-faulting twice in the third game, in which he was broken to love.
Roger Federer produced a near-flawless performance as he avenged his Wimbledon defeat by Novak Djokovic and qualified for the last four of the ATP Finals with a 6-4, 6-3 victory on Thursday.
The Swiss started the tournament with a chastening straight-sets defeat to Dominic Thiem but found his best form when it mattered.
Defeat for the second seed spells the end of his bid to overtake Rafael Nadal and finish as year-end number one.
Roared on by a raucous packed house at London's O2 Arena, six-time champion Federer looked in the groove from the start, cranking up the pressure on Djokovic's serve and dropping just three points on his own serve in the first set.
The Serbian upped his game at the start of the second set but Federer, 38, saved the one break point he faced and broke twice to canter to victory.
The third seed, making his 17th appearance at the ATP Finals, is into his 16th semi-final at the year-end event.
Djokovic needed to win the title to have a chance at knocking Nadal off the top spot, but now the Spaniard is guaranteed to finish the year as the top-ranked player for the fifth time, tying him with Federer, Djokovic and American Jimmy Connors.
"Great atmosphere, great opponent," said Federer, who hit 23 winners and made just five unforced errors. "It was definitely incredibly special. I enjoyed it from the beginning.
"I played incredible and I knew I had to because that's what Novak does. It was definitely magical."
Speaking about what was different from the Wimbledon final, where he squandered two championship points on his own serve, he said: "I won match point I guess.