The American fell behind 5-2 in the first set but used powerful ground strokes to break Kudryavtseva twice and a serve that averaged 162.5 kph (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 first two or three games I was nervous,'' she said. "It was kind of just the first few games of just hitting the ball and feeling it and really getting into a rhythm that made me feel a lot better.''
The youngster could face the tournament's top-seeded player, ninth-ranked Nadia Petrova, in the second round. The Russian opens play Tuesday against Olga Govortsova.
"I actually got into tennis because of Venus and Serena (Williams),'' Keys said. "I was watching Wimbledon one year and Venus was playing and I really liked how she was playing but I also liked her outfit.
"I told my dad I wanted a dress like Venus' and he said, 'Only if you play tennis.' So, I went to Walgreen's, got a racket and started playing.''
Play was hampered by winds that gusted to 56 kph (35 mph).
"I'm kind of used to it but the wind would gust and you wouldn't know what was going to happen to the ball,'' Keys said. "You just really had to move your feet.''
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.
