Alaba passed back to Ramazan Ozcan from the edge of the area without looking, leaving the goalkeeper out of position and desperately scrambling as the ball rolled into the net.
Austria, who face Hungary, Portugal and Iceland in Group F at next month's finals in France, coasted to victory after scoring twice in the opening 20 minutes.
Marko Arnautovic scored after four minutes when he pounced on a defensive mistake and Alessandro Schoepf ran on to a superb Zlatko Junuzovic pass to fire the second in the 18th minute.
Austria took their foot of the pedal after that and a few jeers rang around the stadium after a disappointing second half.
"We must make better use of our chances," said Austria coach Marcel Koller. "I would like to have seen more goals but at least we won. I'm not anxious and we are on the right path."
Koller also said 20-year-old Valentino Lazaro had been left out as he confirmed his 23-mean squad.
Goalkeepers: Robert Almer (Austria Vienna), Heinz Lindner (Eintracht Frankfurt), Ramazan Ozcan (Ingolstadt)
Defenders: Aleksandar Dragovic (Dynamo Kiev), Christian Fuchs (Leicester City), Gyorgy Garics (Darmstadt), Martin Hinteregger (Borussia Moenchengladbach), Florian Klein (VfB Stuttgart), Sebastian Proedl (Watford), Markus Suttner (Ingolstadt), Kevin Wimmer (Tottenham Hotspur)
Midfielders: David Alaba (Bayern Munich), Julian Baumgartlinger (Mainz 05), Stefan Ilsanker, Marcel Sabitzer (both Leipzig), Jakob Jantscher (FC Lucerne), Zlatko Junuzovic (Werder Bremen), Alessandro Schoepf (Schalke 04)
Forwards: Lukas Hinterseer (Ingolstadt), Rubin Okotie (TSV Munich), Marc Janko (FC Basel), Marko Arnautovic (Stoke City), Martin Harnik (VfB Stuttgart)
