Sock showed little sign of fatigue against Cilic and, as well as claiming his own debut victory at London's O2 Arena, he became the first American to triumph at the ATP Finals since Andy Roddick in 2007.
Zverev was slated to face second-seeded Roger Federer later Tuesday in pool play. 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 play a different style and there's always a lot going on, I don't even know what I'm going to do sometimes, it keeps it fun".
"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".
The 19-time Grand Slam champion broke in the first game of the second set to establish an iron grip on the round-robin match but Zverev hit back in the fourth to get back on level terms.
Zverev and American Jack Sock will now battle it out for a place in the last four but Cilic has been knocked out of contention. "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". As the world's most formidable player on clay, Nadal has in the past suggested it would be better if the season-ending Tour Finals at least occasionally took place on his preferred surface.
Serve dominated the rest of the set but Cilic edged 4-2 up in the tie-break when the ball struck the net chord and Sock failed to dig it over.
"It was a good battle and I always enjoy myself at this attractive arena", said Federer, who has now reached the semi-finals 14 times.
"Definitely not a great record, but I felt that I played even well past year", Cilic said.
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. "It's an fantastic atmosphere, you make me feel like home".
"It's definitely disappointing in both matches in that third set after being in a good position and putting myself in a good position".
"But unfortunately I didn't close it". I'm here to win matches.