The U.S. Open runner-up burst out of the blocks and wrapped up the first set in just 25 minutes under the blazing sun on Court Philippe Chatrier.
Kudryavtseva, the world number 78, stopped the rot by winning the eighth game and had the audacity to break for a 2-1 lead before Wozniacki, 19, restored order, making the decisive break in game eight for a 5-3 lead.
She sealed the win after an hour and nine minutes when the Russian netted a backhand service return. She now plays Germany's Kristina Barrois or Italy's Tathiana Garbin for a place in the third round.
(Editing by Miles Evans)