The Swiss, a six-time winner of the event, was always in control of the Group Boris Becker clash against the tournament's surprise package.
Sock, who made the cut after winning the Paris Masters, did manage to shake off his early nerves to produce a commendable showing, particularly in the second set, but Federer was ultimately too strong.
Having won the toss, the 19-time grand slam champion – who has not won the Finals since 2011 – elected to make Sock serve first and it paid dividends with an immediate break to set the tone.
With Federer so quickly into his groove, the scale of the task facing Sock was evident and the American did at times look overawed by the occasion.
Even after racing into a 40-0 lead in the fifth game, Sock was taken to deuce before finally fending off the threat.
There was a moment of levity towards the end of the first set when Sock, who had messed up an attempted drop shot, showed his posterior as a supposed target for Federer, who proceeded to hit the net.
Both players saw humour in the incident, but it was Federer smiling when he wrapped up the set a matter of minutes later.
Sock started the second set in style, holding to love in a game sealed by a stunning cross-court forehand that left Federer stranded.
The 25-year-old underdog provided prolonged resistance and dug deep to fend off five break points across three service games to lead 6-5, putting pressure on his illustrious rival.
Federer coolly took it to a tie-break, where he eased over the line to secure a deserved win.