Goffin will next play Romanian qualifier Marius Copil, who ended the challenge of another Belgian, Steve Darcis, 7-6 (3), 6-2.
Briton Kyle Edmund beat second-seeded Spanish veteran David Ferrer in a third-set tiebreak to set up a quarterfinal with Andreas Seppi of Italy.
The No. 43-ranked Edmund dominated the first set, before Ferrer recovered to take the second. But Edmund prevailed in the third for a 6-1, 3-6, 7-6 (3) victory in just over two hours.
Earlier, fifth-seeded Gilles Simon of France lost to Jan-Lennard Struff of Germany 6-4, 6-4.