It took Djokovic one hour and 54 minutes to overcome his fellow veteran, and the Serbian admitted afterwards that he “struggled to find rhythm”.
The world No. 5 said: “I (lacked) some matches – my last one was at the US Open – so I got a really tough opener against Marin, who, when he is feeling the ball, is so dangerous and can beat anybody.
“I did enjoy it, but I also suffered a lot on the court. It was a very close match.”
Djokovic added: “He was probably the better player for the first set, and he didn’t give me time to breathe.
“I think I dug myself out of trouble with good serving, which obviously makes me happy.”
With Cilic only a year younger than Djokovic, their combined age of 75 years and 139 days was the oldest of any opponents in an ATP Masters 1000 main draw match.
There was little to split the players in the opening set, both holding serve until Djokovic eased to victory in the tie-break.
Djokovic claimed the first break of serve of the match in the third game of the second set, before holding his serve for the remaining games to seal victory.
The world No. 5 will now face German qualifier Yannick Hanfmann in the third round as he targets his first tournament win since claiming his 100th ATP singles title with victory in Geneva in May.
