Six-time champion Roger Federer opened with a straight-set win over Jack Sock at the ATP Finals in London.
The 36-year-old Swiss, making his 15th appearance at the season-ending event for the top eight players in the world, won 6-4 7-6 (7-4) at the O2 Arena.
American Sock was making his tournament debut, having qualified by winning the Paris Masters a week ago.
Alexander Zverev beat Marin Cilic 4-6 6-3 6-4 in Sunday’s second round-robin match in the Boris Becker Group.
German third seed Zverev broke serve in the opening game with a deft volley and took the first set, but Croatian fifth seed Cilic grew stronger as the match progressed and looked set for victory at 3-1 up in the decider.
However, 20-year-old Zverev showed why he has won two Masters titles this year as he reeled off five of six games, breaking serve to love to clinch victory.
“For the most part of the second and third sets he was the better player, I was just happy to come back and get the win,” said Zverev.
The Pete Sampras Group starts on Monday, with Dominic Thiem taking on Grigor Dmitrov at 14:00 GMT followed by Rafael Nadal against David Goffin at 20:00. Jamie Murray and Bruno Soares begin their doubles campaign at 12:00.
Defending champion Andy Murray, five-time winner Novak Djokovic and three-time Grand Slam champion Stan Wawrinka are among a number of players who chose to end their seasons early to recover from injuries.