The fifth-seeded Roddick, who had a bye in the opening round, beat fellow American James Blake 7-6 (8-6), 7-6 (8-6) on the hard courts at Wake Forest University.
Qualifier Goffin rallied past 10th-seeded Serbian Viktor Troicki in a 3-6, 6-4, 7-5 upset.
Seventh-seeded American Sam Querrey and was leading Santiago Giraldo of Colombia 6-3 when their second-round match was suspended due to rain.
In first-round action Monday, Donald Young snapped a 17-match losing with a 4-6, 6-3, 6-2 win over Argentine Leonardo Mayer, while Brazilian Thomaz Bellucci was leading Marcos Baghdatis of Cyprus 7-5, 3-1 when Baghdatis retired.
Other Day 2 winners included Poland's Lukasz Kubot, Ukrainian qualifier Sergiy Stakhovsky, Slovak Martin Klizan, Ernests Gulbis of Latvia, Robin Haase of the Netherlands, American qualifier Michael McClune, Taiwan's Yen-Hsun Lu and German qualifier Benjamin Becker.