It was highly competitive with Zverev more than holding his own, and even threatening to break the World No. 1, but his failure to do so belied a worse fate, as he double-faulted away the set for Djokovic to take the lead.
"I held serve well, I backed it up from the baseline, I played very solid and didn't give him many opportunities".
"I think the date is very important and I think none of the top players will play, except Rafa (Nadal) because it's in Spain".
"I think I'll take it as a normal quarter-final match at a normal tournament", said the German, who beat Cilic in his opening match on Monday. The German eventually forced the first break points of the match with the score level at 4-4 but Djokovic held after a backhand lob from Zverev drifted inches wide.
Breaks of serve were exchanged in the second set before Cilic was required to save a match point at 4-5. I'll try my best to add as much clarity as possible with these, during tomorrow's preview.
In his 11th appearance at the Finals, the Serb will be guaranteed to reach the last four for the eighth time if John Isner beats Marin Cilic or if Cilic defeats Isner in three sets later on Wednesday.
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"I thought I played well from midway through the second set, I started to swing through the ball but I haven't served that great". 6-1, and would go on to win his 32nd Masters title. "So I think creating one event is an ideal scenario and I think outcome for everyone", he said.
The Serb, 10 years older than his opponent, was made to work hard in an absorbing first set but Zverev's challenge crumbled at the O2 Arena as Djokovic won 6-4 6-1. I'm obviously relying on it a lot ever since I was a boy, starting to play tennis and I was skiing a lot in those days and playing different sports.
The next game always looked risky for Zverev and so it proved as he double-faulted to concede the set.
Zverev had finished an otherwise extremely tidy opening set with a first double-fault to hand the initiative to Djokovic, and he simply could not wrestle it back. "If I break him at 4-4, we'll see where the match goes".
"It wasn't a great quality tennis match, to be honest, at least from the court", Djokovic, who was coughing occasionally and grabbing a tissue from his pocket, told reporters.
Zverev's earlier win over Cilic in the round-robin means both those players still have a chance of reaching the semifinals for the first time.