Marin Cilic saw a 3-1 lead in the deciding set count for nothing, as Alexander Zverev won on his ATP Finals debut.
Antonia Lottner was unable to cause an upset as Monica Niculescu won the Open de Limoges.
The ATP Finals title has eluded Roger Federer since 2011, but he started this year's campaign with a win against Jack Sock.
Having only recently returned from wrist surgery, Belinda Bencic added a third WTA Tour title to her collection.
Hyeon Chung maintained his perfect record this week to win his first ATP World Tour title at the expense of Andrey Rublev.
CoCo Vandeweghe won the first point of the Fed Cup final, but 19-year-old Aryna Sabalenka made it 1-1 by beating the US Open champion.
As he continues his recovery from a hip injury, Andy Murray was fit enough to practice alongside Dominic Thiem at the O2 Arena on Saturday.
World number one Rafael Nadal is happy with tennis as it is, yet he is glad the sport is trialling new ideas.
Even at the age of 36, Roger Federer said he was fit – and fresh – ahead of the ATP Finals.
A knee issue forced Rafael Nadal to withdraw from the Paris Masters last week, but the Spaniard feels ready to go in London.