The reigning two-time French Open champion, who is seeking his first title in nine months, beat Argentina's Juan Ignacio Chela. 7-5, 7-5.
Chela had won his last eight matches overall, including a title run in Acapulco two weeks ago.
The other quarterfinals will take place on Friday, when ninth-seeded German Tommy Haas pays 13th-seeded Andy Murray of Scotland; and 12th-seeded Novak Djokovic of Serbia faces 14th-seeded Spaniard David Ferrer.
The 2007 Indian Wells champion will earn $500,000.
Celebrity Families of 2014 [PHOTOS]