Navratilova, given a wild card to play in the tournament, lost her only game after building a 5-0 lead over her 24-year-old opponent in the second set.
The veteran American star hadn't played a singles match at Wimbledon since she lost the 1994 final to Conchita Martinez.
Federer beat British wild card Alex Bogdanovich 6-3, 6-3, 6-0 and No. 7 Lleyton Hewitt of Australia defeated Austria's Jurgen Melzer 6-2, 6-4, 6-2. Other men's winners included Juan Carlos Ferrero of Spain, Jonas Bjorkman of Sweden, Goran Ivanisevic of Croatia, Sebastien Grosjean of France and Robby Ginepri of the United States.
In addition to the second-seeded Myskina and the No. 3 Williams, women advancing included No. 5 Lindsay Davenport of the United states, Ali Sugiyama of Japan and Vera Zvonareva and Maria Sharapova of Russia.