Austria lie third in Group 7 on 10 points, four behind France and a further four adrift of group leaders Serbia. The home side took the lead in the first minute through Stefan Maierhofer and Janko then netted 15 minutes later to double the advantage.
Janko got his second from the penalty spot after 59 minutes before Andreas Olsen netted a consolation for the visitors seven minutes from the end. The home side made the perfect start as Wolves striker Maierhofer struck after 49 seconds as he finished from five yards from a cross from the left wing by Jakob Jantscher.
Maierhofer missed the chance to add a second four minutes later as he shot wide after a shot from Janko had been beaten away by Faroes goalkeeper Jakup Mikkelsen. Austria doubled their lead when Janko shot home from close range after Daniel Beichler had crossed low from the right.
The visitors had their first chance after 37 minutes but Christian Holst did little to trouble Austrian goalkeeper Helge Payer. Janko went close to getting a third for Austria when he collected a cross from Jantscher and turned before shooting only to see Mikkelsen save with his left foot.
Beichler set up Maierhofer for another chance but the striker's shot was again saved by Mikkelsen. However, a minute later Janko did make it 3-0 when he sent the keeper the wrong way from the penalty spot after midfielder Andreas Hoelzl was brought down by Atli Gregersen.
Mikkelsen pulled off another save when he kept out a free-kick from Jantscher. Christian Fuchs set up two chances but Franz Schiemer and Janko were both wide of the target.
The Faroes pulled a goal back in the last 10 minutes when Bogi Loekin set up Olsen whose shot was deflected past Payer off Aleksandar Dragovic.