Federer has always thrived on the indoor hard-court used at the O2 Arena, as he showed once again by kicking off his bid for a seventh title at the event with a 6-4, 7-6 (7/4) win over Jack Sock on Sunday.
He may still have to beat Zverev in his final group match to qualify, with the talented German going up against favourite Roger Federer later on Tuesday.
With these two powerful customers desperate to keep their hopes alive after losing their opening matches, it was the American, in his debut finals, who held his nerve best in the decisive tiebreak after a compelling 2 hours 27 minutes contest.
However, Federer overcame the 20-year-old in an error-strewn affair, with both making close to 40 unforced errors - not that the Swiss will be concerned by those figures right now.
The world No. 3 came out firing.
Sock claimed five points in a row to set up two match points and he converted the first when a Cilic backhand floated long.
Federer and Zverev had already met in the O2 Arena - when the German's practice session overran and his opponent was forced to bounce on his toes for a few minutes while Juan Carlos Ferrero put his man through the last couple of serves.
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"He didn't hit many down-the-line winners during the match".
The tension returned in the final game of the set, with Zverev facing multiple break points amid distractions from the crowd and celebrating a point he'd thought he'd won only to be overruled by Hawk Eye, but he got the hold nonetheless to force a breaker in the first.
Zverev's response to finding himself behind was not ideal.
The Swiss legend is now through to the semi-finals for the 14th time and there would appear to be little in the way of stopping him.
But Zverev went to pieces in the tie-break, only to fight back from 2-0 down in the second, capitalising on a noticeable Federer dip including five consecutive missed serves.
However, like a soft push at a scrum, the lack of resistance from Zverev all of a sudden seemed to throw Federer off-balance and he presented three break point opportunities in the fourth game of the set with two consecutive double-faults.
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.