Keys, of Boca Raton, Fla., fell behind 5-2 in the first set but used powerful ground strokes to break Kudryavtseva twice and a serve that averaged 101 mph to win the set.
Keys lost the first game of the second set before going on a four-game run, and after the 81st-ranked Kudryavtseva fought back to 4-5, Keys won the set with an ace.
The youngster could face the tournament's top seed and the world's ninth-ranked player, Nadia Petrova, in the second round. The Russian opens play Tuesday against Olga Govortsova.
Other ranked players in the field include No. 12 Caroline Wozniacki, No. 16 Dominka Cibulkova, who lost in last year's final to Maria Sharapova, and 43rd-ranked Daniela Hantuchova.
In other early matches, Kateryna Bondarenko of the Ukraine beat Barbora Zahlavova Strycova of the Czech Republic 7-6 (2), 6-2.
This year's tournament, being played at Sawgrass Country Club, has been downsized to go with its new sponsor and a move to a new site.
The tournament, formerly sponsored by Bausch & Lomb, moved from its longtime home in Amelia Island to Ponte Vedra Beach. The total purse dropped from last year's $600,000 to $220,000 with the winner receiving $37,000.
Last year's winner, Maria Sharapova, isn't playing. Other former champions of the tournament include Martina Navratilova, Chris Evert, Steffi Graf, Lindsay Davenport, Monica Seles and Venus Williams.
