He eventually emerged after nearly two and a half hours with a 5-7, 6-2, 7-6 (4) win - the first by an American in singles at the event since 2007 - having several times come back from what looked like hopeless positions.
Cilic, who won the 2014 U.S. Open, broke the American twice to win the first set but found himself adrift in the second as Sock levelled the round-robin match with two breaks of his own.
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 think I first qualified for this tournament in Shanghai in 2002 when I was 21, so I'm very excited for Alex - he has a very bright future ahead of him".
The Croatian led Sock by the same margin in the decisive set on Tuesday and was 4-2 up in the tie-break, but the eighth seed from America refused to be beaten and has now won all three matches against Cilic.
Cilic looked set to come out on top when he claimed the first mini-break of the tie-break, but Sock showed incredible athleticism to dart in and guide away a victor after a Cilic shot struck the net cord and he won five points in a row to seal a hard-fought victory. Plus, he loves playing under a roof, which favours his pure ball-striking talent.
The top two players from each of the two groups of four will progress to the semi-finals. I'm relieved that in the last match I can play freely against Cilic.
"It was a tough one for sure", Sock said after defeating Cilic for the third time in as many attempts.
"He had a really nice season, especially the beginning, now the end". "The fire alarm went off in our hotel at 4am this morning".
The ageless Swiss resisted a sprited challenge from German prodigy Alexander Zverev to close in on an unprecedented seventh season-ending championship with a 7-6 (8-6) 5-7 6-1 victory on Tuesday night. I'm here to win matches. "In those three matches that I played, I had good chances at least to win".