With Germany already qualified from Group C and Sweden guaranteed the play-off place the match was a dead rubber, but the visitors finished strongly with goals from Andreas Ivanschitz and Sebastien Prodl, with David Alaba scoring the third from the penalty spot.
Ivanschitz opened the scoring for Austria in the 16th minute when he turned in Martin Harnik's cross from close range.
The Faroes had Christian Holst's chance blocked by defender Prodl soon after. Alaba was denied by Faroes goalkeeper Gunnar Nielsen before Austria goalkeeper Heinz Lindner sent Pol Johannes Justinussen's shot over the bar.
However, the home side were not able to find the breakthrough, with Austria killing off the game through Prodl's 64th-minute strike and Alaba's penalty three minutes later after Frodi Benjaminsen fouled Martin Harnik.