The Swiss ace, who is making his 15th appearance at the end-of-season event, secured a 6-4 7-6 victory over his American opponent who, in contrast, was making his tournament debut following his victory at last week's Paris Masters.
Federer never looked in danger of losing the match after Sock dropped his opening service game and the world number two believes that fast start helped him take control of the rest of the contest.
"I got off to a great start, my big hope was I was going to be able to play a bit more freely after that," said Federer.
"The second set was tight, I missed some opportunities, the breaker could have gone either way and in the end he helped me with some double faults and some mistakes."
The 19-time major winner has now moved to the top of the Boris Becker group and he admits he is making up for lost time at the event, after he was forced to miss the tournament last year due to injury.
"It's wonderful to be back, especially after missing last year with injury," he added.
The other two players in the group, Marin Cilic and Alexander Zverev will get their campaigns underway when they go head-to head at London’s O2 Arena on Sunday evening.