In a see-saw deciding set, the Croatian fifth seed started quickly and raced to a 3-0 lead before Sock, the eighth seed, steadied himself, cancelling out the break.
The defeat was another heartbreaking loss at The O2 Arena for Cilic.
The next break point didn't come until the 11th game.
The ATP Finals feature the top eight fit male singles players and doubles teams who have accrued the most points throughout the 2017 season.
"I mean, I did it more for fun", he says. "When he's playing well, he's definitely very unsafe".
Jack Sock has revealed that he was forced out of his room at 4am on Tuesday morning due to a fire alarm at his hotel.
The opening match in the Pete Sampras Group produced a feast of stylish backhands from both players but it was Dimitrov, the first Bulgarian to qualify for the tournament in its 48-year-old history, who overcome some late jitters to prevail.
"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", Sock said after the two-hour, 28-minute match.
"I think Jack is playing really good", Cilic said.
The American No 1 increased his advantage in the second set with a further break of the Cilic serve to move 4-1 ahead before he served out in style with an ace to force the deciding third set - the fourth time already this week that a match has gone the distance.
"I'm not the type of guy that will just enter a draw and be happy to make the third round or the quarters or whatever".
"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". My coach growing up nicknamed me "Showtime" because I love playing in front of people, and there is always a lot going on.
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