Roddick, who was handed a first-round bye at the ATP tournament at Wake Forest University, clinched both sets on close tie-breaks to set up a third-round meeting with either Steve Darcis or Denis Istomin.
Number 10 seed Viktor Troicki was the biggest name to fall on day two of action, the Serb stunned by David Goffin, who won 3-6 6-4 7-5 to progress into the third round.
Earlier in the day, the first-round schedule was completed, with Marcos Baghdatis bowing out at the first hurdle after the Cypriot retired hurt when 7-5 3-1 down against Thomaz Bellucci.
All four qualifiers went through in the afternoon session, with Michael McClune beating Alejandro Falla 6-1 6-4, Ernests Gulbis downing Carlos Berlocq 6-4 7-5, Benjamin Becker seeing off Tatsuma Ito 6-3 4-6 6-2 and Sergiy Stakhovsky winning 7-6 (4) 6-4 against Gilles Muller.
Donald Young ended his lengthy losing streak - which stretched back 17 games to February - with a 4-6 6-3 6-2 win over Leonardo Mayer, while Robin Haase joined him in the second round after sending Nikolay Davydenko packing 6-2 6-3.
Other first-round winners included Lukasz Kubot, Lu Yen-Hsun and Martin Klizan.