A largely even encounter swung in favour of Marcel Koller's men in the closing stages and their pressure was rewarded when Alaba - who scored an injury-time equaliser when the sides last met in March – fired home the only goal of the game from close range.
Austria now sit three points behind second-placed Sweden in Group C with two games remaining, while Ireland are a further three points back and effectively out of the running.
The pressure on Ireland boss Giovanni Trapattoni, who has already admitted that he does not expect to continue beyond the current campaign, is sure to intensify in the wake of this defeat.
There were two changes to Ireland's line-up, Anthony Pilkington making his full debut on the left wing in place of James McClean and Paul Green taking over from the injured Glenn Whelan in central midfield.
Sebastian Proedl, Guido Burgstaller and Julian Baumgartlinger came into Austria's side at the expense of Emanuel Pogatetz, Andreas Ivanschitz and Marko Arnautovic.
Neither side offered any real attacking threat in a dour opening to the game, although the visitors initially dominated possession.
The first chance of note eventually arrived in the 29th minute, Ireland's Robbie Keane firing across goal from a narrow angle to bring much-needed life to proceedings.
A clever chip from Alaba provided Andreas Weimann with an opportunity moments later but the Aston Villa forward was unable to bring the ball under control.
Pilkington then fired into the side-netting for Ireland before Alaba skipped past Richard Dunne and tested David Forde from 22 yards.
Forde had to be alert again to keep out Martin Harnik with his feet after another effort from the lively Alaba had been blocked.
John O'Shea was booked for a foul on Weimann shortly before the break - ruling him out of next month's meeting with Germany - and came off with an ankle injury early in the second half.
That preceded a promising spell for Ireland that saw Jonathan Walters, Shane Long and Marc Wilson all fail to hit the target from distance, the latter going close on two occasions.
Richard Dunne followed central defensive partner O'Shea in picking up a suspension when he was booked for handball, while Austria’s Arnautovic went close with a speculative lob not long after coming off the bench.
The hosts should have taken the lead after 66 minutes when Christian Fuchs' cutback found Weimann unmarked 12 yards from goal. However, the striker fired his first-time shot straight at Forde.
Harnik also proved wasteful when flashing a powerful strike past Forde's near post.
Arnautovic then saw a header cleared off the line by Green prior to Ireland full-back Seamus Coleman blocking two goal-bound shots in quick succession during Austria's best spell of the game.
The hosts eventually gained the breakthrough in the 84th minute, Alaba blasting past Forde after Ireland failed to clear a low cross from the left.
