Despite serving up 15 aces, Soderling, who lost to Roger Federer in last year's French Open final, was broken three times.
"I'm really happy with the way I played," Rochus said. "Robin didn't play his best tennis but tactically I played very good, I did a lot of drop shots and I used my slice well."
World No. 7 Soderling was handed a third consecutive defeat after his third-round exit in Rome and an opening-round loss in Madrid last week.
"We knew it was going to be difficult from the beginning," Soderling's coach Magnus Norman said. "Robin is not feeling the ball 100 percent and he doesn't have the confidence he'd like to have. Of course, it's not the preparation he wants going to a big tournament."
The French Open starts on Sunday in Paris.
Rochus, who reached his first quarterfinals of the season, will next play Richard Gasquet of France, who defeated Alexandr Dolgopolov of Ukraine 6-0, 2-6, 6-3.
Second-seeded Fernando Verdasco of Spain, who beat Soderling in the Barcelona final last month, cruised into the quarters with a 6-2, 6-2 win over Frenchman Florent Serra.
Fifth-seeded Marcos Baghdatis of Cyprus also advanced with a 6-3, 6-2 win over Simon Greul of Germany after converting three of his five break point chances.
"I'm playing good tennis, I'm feeling good on court and I'm finding solutions to win," Baghdatis said after conceding only nine points on his serve. "I'm clever on court and I'm happy with that."
Baghdatis' next opponent will be Leonardo Mayer of Argentina, who beat fourth-seeded Thomaz Bellucci of Brazil 6-4, 6-1 to avenge a loss in Rome three weeks ago.
Potito Starace of Italy ousted eighth-seeded Lukasz Kubot 6-3, 6-4, his third straight win over the Pole.