The six-time champion, 36, defeated the American 6-4 7-6 (7-4).
Federer is making his 15th appearance at the season-ending event for the top eight players in the world.
On his part, Sock was making his tournament debut, having qualified by winning the Paris Masters a week ago.
Later on Sunday, Alexander Zverev takes on Marin Cilic in the Boris Becker Group.
The Pete Sampras Group starts on Monday, with Dominic Thiem taking on Grigor Dmitrov followed by Rafael Nadal against David Goffin.