The British No 2, who was dominant at the baseline and consistent with his serve, defeated the former French Open champion, 6-4, 6-3. The Austrian, who suffered a minor leg injury and needed treatment in the first set, never threatened Rusedski after that.
After breaking Muster's serve in the first set, Rusedski did so again at the beginning of the second, and although the home favourite saved one match point while trailing at 3-5, he could not save another as Rusedski broke again for victory.
The world No 17 now faces the winner of Pat Rafter's match against the Swede Magnus Norman.
The No 2 seed, Goran Ivanisevic, followed Michael Chang out of the Singapore Open on Thursday, falling to Australia's Mark Woodforde, 6-4, 7-6 in the second round.
It was the second tournament shock in as many days after the unseeded German, Michael Kohlmann, eliminated Chang, the No 3 seed, on Wednesday.
Woodforde advanced to the quarter-finals only six weeks after losing to the Croat at the US Open.
At Flushing Meadow, the players had exchanged words and criticised each other's games. But this time they were full of mutual respect. "Today my game plan was really to play a decent match against Goran," Woodforde said. "I was ecstatic I won in the tie-break even after I dropped my serve."
At the women's European Indoor Championships in Zurich, the No 4 seed, Nathalie Tauziat, breezed into the quarter-finals by defeating Lisa Raymond, 6-2, 6-3, thus maintaining her record of never having dropped a set against the American.
Dominique Van Roost, of Belgium, who sent Lindsay Davenport to the top of the world rankings when she beat Martina Hingis last week, also progressed to the last eight with a 6-3, 6-4 win over Amelie Mauresmo of France. Van Roost now plays the Romanian Irina Spirlea.Reuse content