The visitors came close to breaking the deadlock with 15 minutes played, but Alexander Kokorin's effort from the edge of the box rattled the post.
Russia threatened again just a minute later when Denis Cheryshev fired off target following a slick move, while Austria's first meaningful opening arrived on 26 minutes as Martin Harnik's low drive was kept out by Igor Akinfeev.
The away side continued to look the more likely to score during the remainder of a cagey first half, but they were unable to land the vital blow as the Austrians held on to go in level at the break.
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Austria started the second period in positive fashion and they could have taken the lead on 51 minutes when Marko Arnautovic's shot was pushed away by the alert Akinfeev.
However, chances became few and far between after that as the two sides were both guilty of committing a series of needless fouls that hampered the flow of the game.
Russia tried to salvage a share of the spoils in the final 15 minutes, but Austria held on to extend their lead at the top of the group.