Rusedski has never played the Russian before and said: "It will be a match between two big servers. I'll have to be serving well and I'll have to go for more on my returns."
He and Stafford both held serve through their first set before Rusedski overwhelmed the South African in the tie-break, losing just one point. Stafford had several chances early in the second set, but Rusedski saved the situation with one of the 13 aces he fired during the 80-minute match.
The French Open winner, Yevgeny Kafelnikov, stepped up a gear to beat Czech Petr Korda 6-4, 6-3 in the second round of the Lyon Grand Prix.
The fourth seed, Marcelo Rios of Chile, and the Swede Thomas Enqvist, seeded fifth, also progressed to the third round, but Thomas Muster, the top seed, and Michael Stich, the No 3, went out. Muster, playing in his first tournament since walking off court in the Davis Cup in Brazil, lost 6-3, 6-3 to the American Chris Woodruff, while Stich went down 6-3, 6- 7, 6-2 to Sweden's Magnus Gustafsson.