The Serbian won over Goffin 7-6 (7-5) 6-4 7-5. "It was not easy. David is a good player with a lot of talent and a lot of aggressiveness," said Djokovic after the match.
Djokovic, who was runner-up last year, will face Argentina's Guido Pella next.
In other matches played on 28 May, former US Open champion ninth seed Sam Stosur thrashed Kimiko Date-Krumm, breaking her 42-year-old opponent five times to win 6-0 6-2 in 64 minutes.
Australian Bernard Tomic retired with an apparent knee injury while trailing Romania's Victor Hanescu 7-5 7-6 (10-8) 2-1.
Women's third seed Victoria Azarenka had her match against Elena Vesnina postponed until Wednesday, as was British number two Heather Watson's encounter with Stefanie Voegele.
