Three-time major winner Murray clinched a 7-6 (7/4), 6-3 win against the world number 10 to move into the quarterfinals.
Murray had also defeated Poland's Hubert Hurkacz, now at nine in the world, in Vienna.
"It was a very tough match. He hits the ball huge from the back of the court so there were a lot of long rallies and a lot of running," Murray told atptour.com.
"But it's probably my best win this season. I want to keep it going now."
Murray, now ranked a lowly 143 in the world, will face Tommy Paul of the United States for a place in the last four.
Paul defeated American compatriot and fifth seed Taylor Fritz 6-4, 6-4.
Defending champion and third seed Denis Shapovalov defeated Italian qualifier Andrea Vavassori 7-6 (7/1), 6-1.
Shapovalov will next face France's Arthur Rinderknech, who won 6-4, 6-1 against lucky loser Jozef Kovalik of Slovakia.
US Open quarterfinalist Botic van de Zandschulp defeated Hungarian seventh seed Marton Fucsovics 7-6 (7/3), 3-6, 7-5.
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