The seventh-seeded Swiss, who has won a record 17 Grand Slam titles, defeated Tursunov 7-6 (9/7), 7-6 (7/2) to take his perfect record against the Russian to 4-0.
Federer, now ranked eighth in the world, surrendered a 3-0 lead in the opening set before prevailing in the tiebreaker.
He recovered an early break in the second set before dominating in the second-set decider.
Federer, who arrived in California after victory in the Dubai tournament for his 78th career trophy, awaits the winner of Monday night's match between 11th-seeded German Tommy Haas and 19th-seeded Kei Nishikori of Japan.
Roger Federer reaches fourth round at Indian Wells
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