Kafelnikov, who has won the event each of the last four years, cruised past 18-yeqr-old fellow Russian and Davis Cup teammate Mikhail Youzhny, 6-3, 6-3.
Nicolas Kiefer of Germany outlasted Federer, a native of Switzerland, 6-3, 1-6, 7-6 (7-4).
Sweden's Thomas Johansson, the fifth seed, defeated Davide Sanguinetti of Italy, 6-2, 6-3, but No. 8 Nicolas Escude of France lost to Magnus Gustafsson of Sweden, 6-4, 5-7, 6-4.
On the women's side, just two seeded players were in action on Tuesday, and both advanced.
Top seed Martina Hingis of Switzerland plays her first match Wednesday against Sandra Kleinova of Czechoslovakia.
Celebrity Families of 2014 [PHOTOS]