The two sides are level on 11 points and know that victory would pile the pressure on Sweden, who sit in second place
Both teams are currently level on 11 points in Group C, three behind second-placed Sweden, who came away with a hard-fought 2-1 victory over Giovanni Trapattoni's side in Dublin on Friday.
Austria, meanwhile, go into the game in Vienna following a 3-0 defeat to runaway leaders Germany.
A place in the play-off round for Brazil 2014 is still possible for Ireland and Austria, but both need three points from the clash at the Ernst-Happel-Stadion to keep their hopes of catching Sweden alive.
Ireland's task will be made all the more difficult by the fact that they have not won a competitive fixture in Austria since 1958, but Marcel Koller's men had to rely on a late David Alaba equaliser to secure a 2-2 draw in the reverse fixture in Dublin in March.
Trapattoni has named Anthony Pilkington and Paul Green in his starting side to face Austria. Glenn Whelan has been forced to withdraw from the squad with a hamstring injury, while Pilkington will replace Wigan Athletic winger James McClean, who drops to the bench.
Speaking ahead of Tuesday's fixture, Trapattoni admitted he is unlikely to continue as manager after the nation's World Cup campaign.
"I don't expect after this campaign, to go again with Ireland," he said.