After Sock's win, Federer can claim his 14th year-end semi-final from 15 appearances at the season wrap-up if he beats Zverev, 16 years his junior, in straight sets.
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.
"It was a tough one for sure", Sock said after defeating Cilic for the third time without a defeat in their series.
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Sock claimed five points in a row to set up two match points and he converted the first when a Cilic backhand floated long.
"It's been an interesting morning so far, the fire alarm went off at 4am and we had to exit the building". It is what it is, you have to deal with it. Marin's an incredible player, he's had an awesome season but I was able to get through. It's an awesome atmosphere here and I love playing in London and in front of the fans here. "I'm excited to excited to keep winning and keep my hopes alive this week".
"My coach nicknamed me showtime when I was young".
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'There's always a lot going on in my game.
ATP Tour Finals debutant Alexander Zverev defeated Wimbledon runner-up Marin Cilic 6-4, 3-6, 6-4 in Group Boris Becker on Sunday.
The season-ending extravaganza ATP Finals ends another memorable year which will be covered via our website www.skysports.com/tennis with live blogs, reports, reaction and expert analysis as the season reaches its climax.
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A win for the world No. 2 against the talented German will elevate Federer above American golfer Tiger Woods in the individual sports prize money charts.