Nemanja Nikolic managed to get away the first real attempt of the Group G clash, striking a solid right-foot shot which ended narrowly over the bar.
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It was the home side who took the lead shortly after, however, as Rubin Okotie found the bottom corner of the net from inside the box to give Austria the breakthrough.
Eight minutes before the interval Simon Vukcevic was provided with a good chance to level up the contest, but he was unable to find the target with his header.
The Brave Falcons stopper had to be alert once more 15 minutes from time to keep out Martin Harnik's curled shot, which looked destined for the back of the net.
Montenegro themselves pushed forward in an attempt to level up the game, but they were unable to break down the home side to ensure that Das Team took all three points.