The two have had some close matches in the past, but this win gave Ulihrach a 5-4 lead in the head-to-head series. Ulihrach also defeated Kafelnikov earlier this year in Doha, Qatar.
Defending champion Tim Henman was looking for a small measure of revenge against Guillermo Canas of Argentina after a five-set loss at this year's French Open, but the British fan favorite again was on the losing end.
In the only second-round match of the afternoon, Henman was ousted, 3-6, 7-6 (7-4), 7-6. He had reached the quarterfinals here three times in the previous four years.
American Michael Chang upset Wimbledon champion and fifth seed Goran Ivanisevic, 6-7 (5-7), 6-3, 6-3. Chang is 6-5 lifetime against the Croatian.
Chang's second-round foe will be Austrian wild card entry Stefan Koubek, who also needed three sets to get past qualifier Jiri Vanek of the Czech Republic, 4-6, 6-3, 6-2.
Another Czech, Jiri Novak, fared better against 1999 winner Greg Rusedski, eliminating the Brit, 6-2, 6-2.
Novak meets Tommy Haas in the second round after the sixth-seeded German had a short day. Haas had a 3-0 lead in the first set when France's Jerome Golmard retired with a right knee injury.
In a matchup of unseeded players, Michel Kratochvil of Switzerland defeated Dominik Hrbaty of Slovakia, 7-6 (8-6), 7-5.