The big serving Swede , who won his third career title at the Lyon Grand Prix on Sunday, broke his French opponent once in each set and saved all four break points he faced in the first round match.
However, Soderling could struggle to continue his winning streak given that he is 0-7 against the 13-time Grand Slam champion Federer, who won his 57th career title by winning the Swiss Indoors for the third straight year on Sunday.
Germany's Philipp Kohlschreiber also advanced to the second round after beating Russia's Mikhail Youzhny 6-1, 6-4.
Kohlschreiber had to save eight break points, and next plays fifth-seeded David Ferrer of Spain.
Ferrer is one of several players hoping to grab one of the three remaining places for the season-ending Masters Cup.
Andy Roddick, Juan Martin del Potro and Gilles Simon are also looking to gain enough points to hold their ranking in the top eight and reach Shanghai.
But Ferrer is just behind Simon, with James Blake, Stanislas Wawrinka and Australian Open finalist Jo-Wilfried Tsonga all hoping a good showing will help them qualify for the prestigious year-end championship.
In later matches Tuesday, the seventh-seeded Roddick plays Feliciano Lopez, ninth-seeded del Potro faces Mario Ancic and No. 3 Novak Djokovic - already qualified with Federer for Shanghai - takes on Dmitry Tursunov.
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