Paris's unseasonable downpours kept the world number one off court for most of the day but, after emerging into the early evening gloom, he encountered a talented shot-maker on the other side of the net.
Djokovic came through the first set tie-break thanks in part to the raucous Parisian crowd, whose efforts to inspire his young opponent with an ill-timed shout of "Allez David" at 5-5 on his second serve caused the world number 58 to double fault.
There was a battling quality about Goffin, who managed to break the Serb's serve in the second set and had a break point in the third before succumbing to the six-times grand slam winner.
French Open results (x denotes seeded player):Men:
First Round:
Novak Djokovic (SRB x1) bt David Goffin (BEL) 7-6 (7/5), 6-4, 7-5
Guido Pella (ARG) bt Ivan Dodig (CRO) 4-6, 6-4, 6-3, 2-6, 12-10
Lucas Pouille (FRA) bt Alex Kuznetsov (USA) 6-1, 7-6 (7/2), 6-2
Grigor Dimitrov (BUL x26) bt Alejandro Falla (COL) 6-4, 1-0 - retired
Dmitry Tursunov (RUS) bt Alexandr Dolgopolov (UKR x22) 7-6 (9/7), 6-4, 7-6 (9/7)
Victor Hanescu (ROM) bt Bernard Tomic (AUS) 7-5, 7-6 (10/8), 2-1 -retired
Lu Yen-Hsun (TPE) bt Simone Bolelli (ITA) 6-4, 6-4, 2-1 - retired
Philipp Kohlschreiber (GER x16) bt Jirí Veselý (CZE) 7-6 (7/3), 1-6, 7-5, 6-2
Tommy Haas (GER x12) bt Guillaume Rufin (FRA) 7-6 (7/4), 6-1, 6-3
Jack Sock (USA) bt Guillermo García-López (ESP) 6-2, 6-2, 7-5
Mikhail Youzhny (RUS x29) bt Pablo Andújar (ESP) 4-6, 6-4, 6-2, 6-3
Federico Del Bonis (ARG) bt Julian Reister (GER) 6-7 (2/7), 6-1, 6-0, 6-4
Nikolay Davydenko (RUS) bt Florent Serra (FRA) 6-3, 6-4, 7-5
Denis Istomin (UZB) bt Florian Mayer (GER x28) 4-6, 6-3, 7-5 – retired
Women:
First Round:
Yaroslava Shvedova (KAZ x27) bt Coco Vandeweghe (USA) 6-0, 3-6, 6-2
Marion Bartoli (FRA x13) bt Olga Govortsova (BLR) 7-6 (10/8), 4-6, 7-5
Mariana Duque (COL) bt Kristyna Pliskova (CZE) 6-2, 6-0
Jelena Jankovic (SRB x18) bt Daniela Hantuchova (SVK) 6-4, 7-6 (9/7)
Samantha Stosur (AUS x9) bt Kimiko Date Krumm (JPN) 6-0, 6-2
Alize Cornet (FRA x31) bt Maria João Koehler (POR) 7-5, 6-2
Silvia Soler (ESP) bt Irina Begu (ROM) 6-3, 6-2
Kristina Mladenovic (FRA) bt Lauren Davis (USA) 6-0, 7-5
Dominika Cibulkova (SVK x16) bt Lesya Tsurenko (UKR) 6-1, 6-4
Marina Erakovic (NZL) bt Elena Baltacha (GBR) 6-3, 6-0