Earlier a first-half brace from Jon Walters looked to have won the game but Giovanni Trapattoni's side could not hold on for the win which would have lifted them into second place in Group C behind runaway leaders Germany.
Alaba served Austria's attacking intent when his second minute free-kick from distance went just wide of David Forde's right post.
The visitors then took the lead on 11 minutes when Ciaran Clark was caught with the ball by Zlatko Januzovic.
He ran into the right side of the box before crossing into the centre for Martin Harnik to slot home past the advancing Forde.
But Trapattoni's side were back on level terms 14 minutes later when Walters scored from the penalty spot after Shane Long had been felled by Emanuel Pogatetz in the box, although the defender had not needed to make the challenge.
Long then hit the post with an audacious back-heal from 12 yards before Walters got his second goal in first-half stoppage time after losing his marker and heading in off the post from Glenn Whelan's corner.
Soon after the re-start, James McClean shot at goal from a free-kick but it went into the side-netting.
But Austria were still dangerous, Harnik forcing Forde into a save before Gyorgy Garics shot wide from 10 yards.
At the other end, Heinza Lindner made a great reaction save from a corner as Ireland pushed for a third goal to win the game.
Late on, Trapattoni brought on Paul Green for Long as he tried to protect Ireland's lead but Alaba had the last word with a shot from outside the box in stoppage time which took a slight deflection off substitute Sean St Ledger into the roof of the net.
Ireland now sit fourth in the qualification table - level on points with Austria and Sweden - behind group leaders Germany.