Goffin ousted seventh-seeded Xavier Malisse 4-6, 6-2, 6-3. He lost his serve just once and had three breaks in the final two sets in advancing.
Sugita was a 6-3, 6-4 winner over No. 8-seeded Olivier Rochus by saving six of the seven break points he faced. He won almost three-quarters of the points when he landed his first serve.
Go Soeda capped Tuesday's play with a 6-2, 6-7 (4-7), 7-5 win over Frederico Gil. Both players won 80 points over the second and third sets, but Soeda was able to finish off both is his break opportunities in the third set for the win.
Also Tuesday, Andreas Beck defeated Vasek Pospisil 6-3, 7-6 (10-8); Edouard Roger-Vasselin handled Eric Prodon 6-4, 6-3 and Victor Hanescu beat Sam Querrey 6-3, 6-4. Other first-round results saw Lu Yen-Hsun sweep past Thiemo De Bakker and Steve Darcis advance over Blaz Kavcic.