Agassi, who ended a disappointing and frustrating 1997 ranked 122nd in the world, climbed to No 40 on the strength of his convincing victory over Australian Jason Stoltenberg in Arizona on Sunday.
With the 7-6, 6-4 win over Woodbridge, Agassi stretched his winning streak to 11 matches, during which he has dropped only one set.
The top eight seeds, led by the world No 1, Pete Sampras, have first- round byes in the tournament, the first of the Super Nine events of 1998.
Steffi Graf, trying to force her way back to the top, cruised into the quarter-finals of the Evert Cup, also in Indian Wells. Graf, 28, playing only her second tournament after a nine-month injury absence, needed just 46 minutes to overwhelm Japan's Ai Sugiyama 6-0, 6-1.
"I didn't think I would go out and play like that. It felt great. I was going for my shots, played very deep. It felt pretty good," she said.