Roddick had 26 aces and won 80 percent of the points on his first serve, but the 2003 U.S. Open champion missed five chances to break Ginepri in the second set, including at 5-5.
In the tiebreaker, Roddick was able to convert his first match point.
The seventh-seeded Soderling advanced with a crushing 6-1, 6-2 win over Christophe Rochus of Belgium. Rochus failed to win a single point on the Swede's first serve in the opening set.
Soderling had 20 aces - compared to just one for Rochus - and broke him twice in each set. Soderling saved the only break point he faced in the second set.
Later, second-seeded Richard Gasquet of France plays Steve Darcis of Belgium, and No. 3 Jo-Wilfried Tsonga takes on Fabrice Santoro.
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