Rusedski, seeded seventh, served 10 aces and never faced a break point in a 6-1, 6-3 victory over the Australian, Richard Fromberg.
While Rusedski cruised through, a somewhat rusty Pete Sampras began his quest to regain the No 1 ranking in the world with a straight-sets victory.
The American beat his compatriot Tommy Ho 6-4, 6-3 in his first match since his surprising defeat to Mark Philippoussis in the third round of the Australian Open. "I feel pretty comfortable with my game right now," the world No 2 said.
During his service games in the first set, the left-handed Ho had Sampras on the ropes from the baseline by consistently exploiting the top seed's backhand. But Ho failed to convert break points in the third and fifth games and committed two unforced errors while serving at 5-4 to hand Sampras the first set.
Sampras seemed to pick up his game in the second set, serving and volleying more efficiently and committing fewer errors.
Sampras, who must win the tournament to regain the top ranking from Thomas Muster, challenged the Austrian's right to be called the best in the world. "What Thomas did last year was phenomenal," Sampras said of the 12 1995 titles won by Muster, who on Wednesday in Dubai lost his first match since gaining the top ranking.
"He's by far the best player of the world on clay. But as far as the best player on anything but clay, I don't accept that quite as much."