It was the team's second yellow jersey of the day on Wednesday with Fabian Cancellara not threatened at the Tour de France.
"I'm super happy with this win and the overall," said Fuglsang following the 141.3km stage. "It is certainly defendable and we're going to do everything we can to bring the yellow home. It's cool that the team has the yellow jersey in two different stage races."
There are four stages remaining in Austria.
Overnight leader Danilo Di Luca (Acqua & Sapone) was put under pressure from the outset by RadioShack-Nissan, with four riders in the break on the Iselberg. The Italian, forced to chase, made contact with the group by the time they reached the Grossglockner. That was the cue for Laurent Didier to attack, forcing Di Luca to again go after RadioShack-Nissan. When he reached Didier, Fuglsang launched with NetApp's Leopold Konig.
"I had to go at that point," explained Fuglsang.
The gap went up again and with 50km to go, the duo's advantage was as much as 3:30.
"König didn't do too much work; I think he was really tired," continued Fuglsang. "But in my mind I knew he could be playing and saving his energy to beat me for the stage, so I was careful. I dropped him on a rolling part with 20km to go."
Fuglsang crossed the finish line in Alpendorf 1:14 ahead of Leopold, enough for the overall lead. Di Luca was sixth across the line and 2:47 down on the Dane.