The Swedish fourth seed, who will compete alongside Roddick at the year-end ATP World Tour Finals in London later this month, now faces unseeded Frenchman Michael Llodra, who upset Russian 10th seed Nikolay Davydenko 7-5, 6-1.
Roddick began the match with three straight aces, but Soderling soon began to find range with his strafing groundstrokes and the American had to save break points in his second, third and fourth service games.
Roddick's resistance was finally broken when, after a pair of double-faults, he netted a backhand in his sixth service game to give Soderling the first break of the match, and the first set duly followed.
Soderling secured a break in the first game of the second set and then saw off a break point to go 2-0 up, before cruising to a victory that avenged losses to Roddick at Indian Wells and Cincinnati earlier this year.
"We've played five times now and we've always had tough matches," said Soderling, who lost in the Roland Garros finals in 2009 and 2010.
"Against Andy it's always a matter of taking the chances you get."
Llodra, who eliminated defending champion Novak Djokovic in the previous round, edged a tight first set against 2006 champion Davydenko before securing an early break in the second and running away with the match.
The 30-year-old left-hander, a member of the French team that tackles Serbia in next month's Davis Cup final, had never previously gone beyond the third round of a Masters event.
Later on Friday, top seed Roger Federer faces Austrian 11th seed Jurgen Melzer as the 16-time Grand Slam-winner attempts to break his Bercy hoodoo by reaching the semi-finals here for the first time in his career.
British third seed Andy Murray takes on last year's beaten finalist Gael Monfils, the French number 12 seed, in the other quarter-final.