With Novak Djokovic and Andy Murray sidelined through injury, Federer is the only genuine star left in London and is the clear favorite to lift his seventh year-end title at the grand old age of 36.
Statistically, the last qualifier for these finals was evenly matched with Cilic during the match, but after a run of seven wins in nine matches, his self-belief was high.
The American - the first from his country to reach the event since Mardy Fish in 2011 - needed 2hrs 28mins to deny the big-hitting Croat in a momentum-shifting match.
Cilic, who has won only one of his eight matches overall at the season-ending tournament, is 0-2 and will be eliminated if Federer beats Alexander Zverev in the late match. You make me feel at home. I'm relieved that in the last match I can play freely against Cilic.
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"I wouldn't be out here playing, competing if I didn't think I could give myself a chance to win tournaments, to be here", Sock said.
The next break point didn't come until the 11th game.
Despite having been forced out of bed in the early hours of Tuesday morning by a fire alarm at his hotel, Sock made a fast start - breaking in the opening game, only to hand it straight back to his opponent.
Trust in raw talent is no guarantee of victory in any sport, and it was tested to snapping point when Roger Federer survived a serious examination of his pedigree to advance to the semi-finals of the ATP World Tour Finals, while Jack Sock also stayed in the race. "I'm excited to excited to keep winning and keep my hopes alive this week".
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Cilic is making his third appearance at the season finale, and was looking to bolster his chances of making the semi-finals for the first time.
"I'm just going to try to be a little bit more stubborn in my preparations maybe for the next match, and hopefully next year".
Sock added he played on instinct when he trailed in the tiebreaker.
Sock twice served well under pressure to stay in the match and despite falling a mini-break behind in the tiebreak recovered to win five unanswered points to claim victory.
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