Four months after winning Wimbledon for a record eighth time just a few miles across London, Federer is back in the English capital aiming to cap a remarkably successful spell by lifting the silverware at the O2 Arena.
In the other match in Federer's group, promising German youngster Alexander Zverev showed his potential with a 6-4, 3-6, 6-4 win against Croatia's Marin Cilic.
When Federer missed last year's Tour Finals through injury, it seemed possible he would never recapture his former glories.
He came into 2017 having missed half of last season due to fitness problems and was without a Grand Slam title since 2012.
But the 36-year-old has enjoyed a stunning renaissance, winning the Australian Open and Wimbledon among seven titles -- more than other male player over the last 11 months.
Federer hasn't triumphed at the season-ending Tour Finals since 2011.
But after seeing off Sock in his group opener, the world number two has now won his last 11 matches.
That dominant streak has already earned him titles in Shanghai and Basel, and he hopes to maintain that hot streak all the way to the Tour Finals crown next weekend.
"It's wonderful to be back, especially after missing last year with injury," Federer said.
"I got off to a great start, but the second set was tight.
"The breaker could have gone either way and in the end he helped me with some mistakes. I'm really happy I got through somehow."
With defending champion Andy Murray, Novak Djokovic and Stan Wawrinka all absent from the Tour Finals due to injury, Federer and Rafael Nadal are the unquestioned headline acts.
Having won the French and US Opens this year, Nadal has matched Federer's unexpectedly dominant run as the old rivals hoovered up all four of this year's Grand Slam crowns.
Nadal is already guaranteed to finish as the year-end world number one for the first time since 2013, making the 31-year-old the oldest man to earn that honour.
But Nadal's hopes of finally winning the Tour Finals for the first time could be hampered by injury.
Nadal, twice a Tour Finals runner-up, is due to open his campaign against David Goffin on Monday, however the Spaniard admits he is still struggling with the knee problem that forced him to pull out of the recent Paris Masters.
Speaking after receiving his year-end number one trophy following the Federer match, Nadal said he is ready to give it a go against Goffin.
"It has been a fantastic season, a very emotional one after all of the things I have been going through in the last couple of years with injury. See you tomorrow on court," he said.