Roddick, the top seed and a three-time winner of the event, survived a difficult battle with Sam Querrey 7-6 (7-4), 6-4. Querrey won last week's tour stop in Los Angeles.
Roddick's quarterfinal opponent will be Ivo Karlovic, who defeated Somdev Devvarman 7-5, 6-1. Del Potro will next meet Robin Soderling, who survived against Marc Gicquel 7-5, 5-7, 6-3.
Another quarterfinal will pit Fernando Gonzalez against Tommy Haas. Gonzalez was a 6-2, 6-4 winner over Wayne Odesnik, and Haas defeated Juan Carlos Ferrero 7-5, 2-6, 6-1.