Nishikori, beaten by Federer in the Paris Masters semi-final earlier this month, gained ample revenge in an event that carries total prize money of $8 million (£6.1 million/€7 million) as he earned a 7-6, 6-3 win. 

The Japanese player showed some of his most indefatigable qualities to claim what was his first set against Federer since last year's Australian Open, and when he broke his opponent's serve to go 4-2 up in the second a more significant statistic hove into view - victory in straight sets.

"It is never easy to play with my idol," Nishikori told BBC Sport. 

"It is always a big challenge against him, so it was great to win today.

"The first match of a tournament is never easy, we were both playing a little bit out especially in the first set, but I think I played the second set better.

"I had to change something against him, I lost twice against him in two months. 

"I played good tennis, using the forehand more and more aggressive and it came together in the second set."

The 37-year-old Swiss, who has 20 Grand Slam titles to his name, is seeking a seventh ATP Finals win, but he will face a steeper gradient now having lost this opening group match.

This was the first time he had lost in straight sets at this event since it took up the round-robin format.

In the opening afternoon singles match Kevin Anderson of South Africa, seeded four, beat Austria’s sixth seed Dominic Thiem 6-3, 7-6.

"It is fantastic to be here, I've worked hard and wanted to get here for so long," said the 6ft 8in Anderson, who is the first South African in 23 years to compete at the season-ending championships.

"I've watched it since I was a kid so to play here in this amazing atmosphere and get a win, I couldn't be more happy."

He celebrated the victory by getting the crowd to join in with singing Happy Birthday to his wife Kelsey, who was watching in the arena.

The action had begun with a doubles match in which Britain's fourth seeds Jamie Murray and Bruno Soares of Brazil beat South Africa's Raven Klaasen and Australa's Michael Venus, seeded sixth, 7-6, 4-6, 10-5.

The event is for the top eight players and with Argentina's Juan Martín del Potro also withdrawing it has left two spaces which Japan's Nishikori and American John Isner have filled.

All four singles players involved on day one are in the group named after Australian star Lleyton Hewitt.

World number one Novak Djokovic, seeking a sixth ATP Finals title, is playing in the group named after Brazilian player Guga Kuerten and is joined by Germany's Alexander Zverev, Croatia's Marin Čilić and Isner.

The top two in each group will move on to the semi-finals in an event that is due to end next Sunday (November 18).

In the meantime, the ATP has introduced at these Finals its Fan Meter, which will record decibel levels throughout the tournament, with displays of the loudest moments being displayed at least once per set in all matches.