Isner had 21 aces but it wasn't enough against his Belgian opponent, who has improved in the rankings to 45th from No. 175.
Isner has gone 4-5 since winning at Winston-Salem in August. The loss hurts his bid to qualify for the World Tour Finals next month, with only the Paris Masters left to play before the season-ending event.
Seventh-seeded Marin Cilic joined Goffin in reaching the quarterfinals with a 6-1, 6-4 victory over Fernando Verdasco, with fellow Croatian Ivan Dodig also winning his second-round match, a 6-1, 3-6, 6-2 win over Australian veteran Lleyton Hewitt.
Gilles Muller of Luxembourg knocked off No. 8-seeded Milos Raonic in the first round, edging the Canadian 7-5, 7-6 (1). Also, reigning champion Marcel Granollers of Spain also beat Czech qualifier Jan Hajek 7-5, 6-4 to advance to the second round.