Austria were given a man advantage after 33 minutes but it took them a further twenty minutes to make their advantage tell.
Dimitros Ioannou was red carded for his second booking and this put the home side onto a retreat from which they never recovered earlier momentum.
Harald Cerny struck twice in eight minutess during the second half to all but kill the game for the visitors. His low drives on 54 and 62 minutes gave Austria comfortable control after earlier struggles to break down resistance in front of the Cypriot goal. Hannes Reinmayer added gloss to the scoreline with a long range effort after he cut inside on the run.
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