Goffin, who had a bye into the second round, next plays eighth-seeded Alexander Zverev of Germany, who beat Lukas Rosol of the Czech Republic 6-3, 6-4.
Zverev's huge serve proved decisive even on the slow clay. He had only five aces but won 31 of 32 of his first-serve points, while never facing a break point against Rosol, who double-faulted four times.
Fourth-seeded Philipp Kohlschreiber eased past fellow German Florian Mayer 6-3, 6-2 to set up a quarterfinal against Juan Martin del Potro, who beat Jan-Lennard Struff of Germany 6-2, 3-6, 6-3 in his second clay-court match in three years. The Argentine is coming back from another wrist injury. He controlled the match until a short rain break, but came back strongly in the third. Del Potro struggled to put the match away, however, wasting four match points at 5-1. But he closed it out in his next service game.
Fabio Fognini of Italy progressed after beating Mikhail Kukushkin 6-3, 7-5, and next faces Jozef Kovalik of Slovakia.
Kovalik, a lucky loser who took the place of the injured Gael Monfils, beat Dutch qualifier Igor Sijsling 6-3, 6-4.