The Russian dispatched Rezai 6-2, 6-1 in a match that lasted only 51 minutes, advancing to the second round on the hard courts at Sierra Madre Tennis Club.
The Frenchwoman committed nine double-faults and won only 36 percent of her second-serve points while Kudryavtseva broke Rezai's serve five times.
In other first-round matches Monday, eighth-seeded Polona Hercog of Slovenia breezed past German Angelique Kerber 6-3, 6-3, and Greta Arn of Hungary downed Czech Sandra Zahlavova 6-0, 6-4.
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