Roddick overcame two set points in the tiebreaker Sunday, erasing one with an ace and the second when Tursunov netted a forehand, and won the final three points in a 75-minute first set. Roddick finished with 11 aces and faced only one break point.
Seeded fifth, Roddick is off to the best start of his career this year at 25-4 and leads the ATP Tour in victories.
He was one of only four American men to reach the third round, and only two U.S. women remained - five-time champion Serena Williams and three-time champion Venus Williams. Both were scheduled to play later Sunday.