The top seed suffered a scare in the first set as Goffin broke him to take a 4-3 lead, but that sparked a 10-game winning streak which gave put the Serbian 6-4, 6-0 up with a one-game advantage in the third.
Goffin made Djokovic work a little hard in the final set but he was still able to close it out 6-2 to seal victory in under two hours.
"He started well. he was dictating the play from the baseline," he told the BBC.
"Things could have gone a different way, who knows what the match would have looked like if I had lost the first set but I was very pleased with the second and third.
"I had a tough match in the third round. Other than that, I've won in straight sets and played really well throughout the tournament.
"It's exactly what I wanted and hopefully I can go in the right direction in the semis as well."