Rusedski was beaten by the former Wimbledon champion Richard Krajicek in the quarter-finals of the world indoor tournament in Rotterdam last week, but this was a much-improved performance from Rusedski, who needed three sets to get past America's Vincent Spadea on Tuesday after he dropped the opening set.
It was Rusedski's second victory over Moya in three matches and he will now play Sweden's Thomas Enqvist, who defeated last year's runner-up, Bohdan Ulihrach of the Czech Republic, 6-2, 7-6.
"I was very pleased with the way I played today," Rusedski said. "I served a lot better, played a more solid overall game and fixed up a few areas I wasn't pleased with."
Rusedski served 12 aces in the 62-minute match, and Moya never had a chance to break his opponent's serve.
Andre Agassi continued his resurgence with a three-set victory over third-seeded Australian Pat Rafter in the third round.
Agassi took an hour and 42 minutes to defeat the US Open champion 6-3, 3-6, 6-2, avenging a four-set defeat by the Australian at Flushing Meadow.
Agassi now faces either his old rival, the former world No 1 Jim Courier, or 20-year-old wildcard Jan-Michael Gambill, who upset the 12th-seeded Australian, Mark Philippoussis, in the first-round.
Meanwhile, the seventh seed, Marcelo Rios, also went through after beating Germany's Nicolas Kiefer 6-4, 6-3. The Chilean will now face another German, Tommy Haas, or world No 2, Petr Korda, who beat him in straight sets in the Australian Open final.Reuse content