Continuing to defy Father Time, Roger Federer has seen off the best of generation next to surge into a record 14th semi-final in 15 appearances at the ATP Finals.
The ageless Swiss resisted a spirited challenge from German prodigy Alexander Zverev to close in on an unprecedented seventh season-ending championship crown with a hard-earned 7-6 (8-6) 5-7 6-1 victory on Tuesday night.
"I'm very relieved. It was a good battle," Federer said after subduing the world No.3 in two hours and 28 minutes.
"I was trying to put a lot of balls into play. There was a lot of defence from me tonight. But it paid off, I'm extremely happy.
"To be through in two matches is great. There is always a lot at stake when you play the top guys.
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"I'll be going out there to win, of course (but) I can now play freely in the last match (against Marin Cilic)."
With Federer safely through to the last four, Zverev and American Jack Sock will square off on Thursday for the other semi-final berth from their four-man pool in the round-robin format.
Sock earlier kept his hopes alive after coming from 4-2 down in the final-set tiebreak to overhaul Cilic 5-7 6-2 7-6 (7-4) to claim his first-ever win at the elite eight-man event.
The first American since Mardy Fish in 2011 to reach the year-end showpiece, Sock needed almost two and a half hours to deny the big-hitting Croat in a momentum-shifting match.
"It was a tough one for sure," Sock said after defeating Cilic for the third time in as many attempts.
"It was an interesting day. We had a 4am fire alarm in our hotel also.
"I'm excited to excited to keep winning and keep my hopes alive this week."
After first-up wins in the other pool, Grigor Dimitrov and David Goffin will clash on Wednesday for the right to join Federer in Saturday's semi-finals at London's O2 arena.
Dominic Thiem and Pablo Carreno Busta, a replacement for injured world No.1 Rafael Nadal, meet in Wednesday's other match, both needing to win to have any hope of making the last four.
