Roddick's fellow-American John Isner also reached the second round in Shanghai after saving match points in two tie-breakers against Polish qualifier LukaszKubot.
In other first round matches, Ukraine's Alexandr Dolgopolov beat Marcos Baghdatis of Cyprus 6-4 6-4 and Spain's Nicolas Almagro defeated Poland's LukaszKubot 7-5 6-2.
Goffin stunned Czech 23rd seed Radek Stepanek in the first round proper, then beat more experienced opposition in veteran Frenchman Arnaud Clement -- playing his home tournament for the last time -- and Poland's LukaszKubot.