The 12th seed will now face Ecuador's Nicolas Lapentti, who thrashed Alex Kim of America 6-0 6-1.
Rusedski lost his only previous meeting with Lapentti on the ATP Tour when going down 6-3 6-3 in Rome in 1999.
Elsewhere, American Andre Agassi returned to winning ways with a comfortable 6-3 6-4 victory over Wayne Black of Zimbabwe.
Agassi, a five-time champion of this event and its top seed, entered the match against Black carrying a rare two-match losing streak.
But he ran Black all over the court and broke serve once in each set to take control of the match.
Earlier, his compatriot, Andy Roddick survived an error-strewn first set before beating Paradorn Srichaphan of Thailand 7-6 6-3.
Hrbaty joy
Chile's former world number one Marcelo Rios, beat a third American, Michael Joyce, 6-2 6-2.
"The way I'm playing, I'm looking forward to my matches and I haven't felt that in a while," injury-plagued Rios said afterwards.
"My backhand hasn't felt this good in a year and a half."
Joining him in the next round are fifth-seeded Dominik Hrbaty of Slovakia, who beat Anthony Dupuis of France 7-6 5-7 6-2 and Jan-Michael Gambill, who made short work of Felix Mantilla of Spain 6-3 6-1.