Djokovic, the 2012 runner-up, defeated David Goffin 7-6 (7-5), 6-4, 7-5 by winning the last three games. Djokovic allowed Goffin just two break chances and ended up winning 72 percent of the points on serve.
He had only three breaks himself, with the final one coming in the 11th game of the third set and setting up a chance for Djokovic to serve out the match, which he did by winning the final four points.
The start of play Tuesday was delayed 2 1/2 hours because of rain and play was suspended for some time in the match before Djokovic could take the court. A final delay about 9 p.m. in Paris led to the suspension of play with three matches still to be decided.
Ninth-seeded Stanislas Wawrinka overcame 50 unforced errors for 7-5, 6-3, 6-7 (1-7), 7-5 win over Thiemo de Bakker while No. 12-seeded Tommy Haas beat Guillaume Rufin 7-6 (7-4), 6-1, 6-3 while only dropping his serve once.
No. 26-seed Grigor Dimitrov was ahead of Alejandro Falla 6-4, 1-0 when Falla became ill and retired from the match. Also, 29th-seeded Mikhail Youzhny got past Pablo Andujar 4-6, 6-4, 6-2, 6-3 by cashing two break chances in each of the sets he won.
Guido Pella claimed the first extended match of the tournament, edging Ivan Dodig 4-6, 6-4, 6-3, 2-6, 12-10.
Other unseeded players advancing to the second round Tuesday included: Nikolay Davydenko, Fernando Verdasco, Jack Sock, Philipp Kohlschreiber, Federico Delbonis, Victor Hanescu, Lucas Pouille, Dmitry Tursunov and Lu Yen-Hsun.