Austria winger Marko Arnautovic set up midfielder Alessandro Schoepf for the only goal in the 28th minute, giving coach Franco Foda his fourth win from four matches since taking over from Marcel Koller in November after the team failed to qualify for the World Cup.
"We have to improve our passing," Russia coach Stanislav Cherchesov told Austrian broadcaster ORF. "We created one, two chances to score but we have to do more."
The match, which was Russia's first abroad since beating Hungary 3-0 in Budapest a year ago, marked the end of the team's 10-day training camp in the Austrian region of Stubaital.
Russia plays Turkey in Moscow on Tuesday in its final warmup game before opening the World Cup against Saudi Arabia on June 14. It also plays Egypt and Uruguay in Group A.
Russia started with high pressing but gradually lost control of the match after 15 minutes. Most of its attacks lacked pace and accuracy, while the defense looked vulnerable.
Leading up to the goal, Vladimir Granat and Fyodor Kudryashov gave Arnautovic time to control the ball and set up Schoepf, who was not marked closely enough by Mario Fernandes and beat goalkeeper Igor Akinfeev with a powerful shot just under the crossbar.
With Manchester United coach Jose Mourinho watching from the stands, Akinfeev denied Austria a second goal when he pushed Arnautovic's free kick wide just before halftime.
Russia's best chance came shortly before the hour mark, but Fyodor Smolov sent his effort just wide.
"We didn't give away much in defense and our forward play was effective. It was a deserved victory," Schoepf said.
Austria, which also beat Russia 1-0 twice in qualification for the 2016 European Championship, will host world champion Germany in Klagenfurt on Saturday and Brazil in Vienna next Sunday.