The two sides are level on 11 points and know that victory would pile the pressure on Sweden, which sits 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, goes into the game in Vienna following a 3-0 defeat to runaway leader Germany.
A place in the playoff 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 it has not won a competitive fixture in Austria since 1958, but Marcel Koller's men had to rely on a late David Alaba equalizer 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," Trapattoni said.