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.
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.
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.
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.
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.
