The world number one only got onto Court Philippe Chatrier just after 1830 (1630GMT) yesterday after a marathon women's match and a four-hour total rain stoppage left him kicking his heels.
But the top seed came out fired-up to beat David Goffin of Belgium 7-6 (7/5) 6-4 7-5 to reach the second round.
"Thanks to all the fans for waiting. It was a good match, David is a good player and has a lot of talent," said Djokovic, who next faces Guido Pella of Argentina.
Djokovic, the runner-up to Rafael Nadal in 2012, would have been wary of the challenge posed by Goffin, who made the last 16 in 2012 after coming through qualifying.
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But the world number 58 lacked the firepower to consistently trouble the world number one.
On a day when 13 matches of the 40 scheduled were held over until Wednesday and three were uncompleted, it was troubled Australian Bernard Tomic who found himself at the centre of attention during the cool and damp afternoon.
Tomic, 20, retired from his first round match against Victor Hanescu with a muscle tear.