Sock blasted a ball into the crowd in frustration, but channeled his anger to break in the first game of the second set and was clearly enjoying himself, moving around the court nimbly as he levelled the match in dominant fashion.
Cilic, playing in his third ATP Finals, made the first breakthrough in the decider to help the Croatian move to a 3-0 lead but Sock recovered his composure to claim three games on the bounce, including a fourth break of Cilic's serve.
"That was a tough one for sure", said the American. The fire alarm went off at 4:00 am and we had to exit the building. "I think if I do the right things and I play the right tennis, I can give myself a chance to play on the weekend of any tournament". "Thank you for making it such a special night", he said.
Gigi Hadid Has Bella By Her Side at Glamour Awards!
Gigi Hadid almost took a tumble in front of the cameras on Monday night - but luckily, her sister Bella came to the rescue. They share photos of Olympia on Instagram all the time, and she's absolutely adorable.
Ultimately, the more experienced Croat Cilic, who has a poor record in the end-of-season finals, proved just too erratic, mixing his 35 outright winners with 37 unforced errors.
The 36-year-old six-times champion may have been giving away 16 years to the man tipped to be the next superstar of the game but Federer proved in a dominant third set that for the moment he remains a cut above his young pursuers.
Federer reached the last four at the season-ending tournament for the 14th time and can have a stress-free showdown against Marin Cilic prior to Saturday's knockout clash.
World number two Federer is now an overwhelming favourite for a seventh crown in the absence of Rafael Nadal, who has pulled out injured.