After failing to win a set in his opening round-robin loss to Roger Federer, it was imperative for Sock to beat Cilic, who was himself seeking a first win after a three-set defeat to Alexander Zverev on Sunday.
The 25-year-old is quoted by BBC Sport as saying: "That was a tough one for sure". "It's been an interesting morning, a fire alarm went off at 4am and we all had to exit our hotel so it was a long morning". But I love playing here in London.
"But I love playing here in London, it's an wonderful atmosphere, you make me feel like home. Even I don't know what I'm going to do sometimes but it keeps it fun and I'm looking forward to the next one".
Dimitrov marks debut with narrow win over Thiem Grigor Dimitrov made a winning start to his maiden ATP Finals when he outlasted Austrian Dominic Thiem 6-3, 5-7 7-5 in a gripping afternoon duel at the O2 Arena on Monday.
There was a jovial atmosphere between the two as they embraced and the youngster suggested a game of "first-to-11, no serves" before Federer got on with his 30-minute hit with towering American Sam Querrey, who is the same height as both Zverev and Marin Cilic.
The Croat was the chief aggressor in the opening frame and - after saving a Sock break point at 5-5 - he converted his own to clinch the set.
Sock, however, grew more assertive, attacking Cilic's second serve, and he broke twice for a 4-1 lead then served out to level up.
The 20-year-old German forced a set point in the opener before fading and losing 7-6, 5-7, 6-1 to the world No 2, who remains standing while the other superstars have fallen around him.
Zverev looked as though he had put the disappointment behind him when he jumped out to 40-0 in his next service game, but once again, the forehand errors came to ruin his day and gave Federer five straight points for the double break.
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 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. Another Cilic shot clipped the tape but this time his opponent was alive to it and flicked it down the line.