Murray did not let a late change of opponent upset him when beating the American Jesse Witten in straight sets in the first round. The 18-year-old Scottish wild card, looking to build on last week's Challenger Tour win in California, progressed in style with a 6-4, 6-2 win over 22-year-old Witten.
But Rusedski had to hold his nerve to beat South Africa's Wesley Moodie after three tie-breaks in their second-round match. The seventh seed lost the first set tie-break 7-4, but bounced back to win the next two 9-7 and 7-2.
Murray needed only 65 minutes to claim his sixth ATP win of the season and never trailed after taking a 3-0 lead in the first set. In the second, he broke in the fifth and seventh games to secure victory.
"For the last month I've played really well," Murray said. "I started at Queen's and, then I played well at Wimbledon and won the Challenger. I was a bit lethargic today during my match. When we got in yesterday, we had to fly through the night and I didn't get much sleep. I didn't play my best, but I came through."
Rusedski, who took the RCA title in 2002, hit 21 aces to Moodie's 18 as both were broken just once in a match which lasted 2hr 24min.
Elsewhere, another of the game's new generation, the Spaniard Rafael Nadal won his 30th successive match win on clay yesterday with a ruthless 6-1 6-2 victory over Hugo Armando in the second round of the Mercedes Cup in Stuttgart.
The French Open champion, 19, was last beaten on the surface in early April in Valencia, and the American qualifier was no match.Reuse content