Vincent Janssen put a young Dutch side in front after nine minutes when the home defence mistakenly thought he was offside, leaving him free to head in Steven Berghuis' looping cross from six metres.
A superbly-worked goal by Georginio Wijnaldum in the second period gave Austria a miserable send-off as they headed for their first major finals since 2008.
The Austria defence was also left red-faced when David Alaba scored an embarrassing own goal in Tuesday's 2-1 win over Malta after passing the ball back to his goalkeeper without looking.
The Dutch had a point to prove after their failure to qualify for the finals in France and, with the hosts wanting to land a morale-boosting win, there were some surprisingly late and full-blooded challenges.
Austria fielded a full-strength side apart from Marcel Sabitzer replacing Martin Harnik on the right of midfield.
The home side made a bright start and were lively going forward but the early goal took the wind out of their sails.
Austria left gaps at the back and had another scare when Quincy Promes hit the post with a deflected shot from 25 metres in the 34th minute.
Promes was a constant menace and set up the second goal when he burst down the left and found Luuk De Jong who laid the ball off for Wijnaldum to sidefoot home in the 66th minute.
Marc Janko had Austria's best first-half chance when he fired into the sidenetting from close range and Alaba blasted over from a similar position just before the Dutch scored their second goal.
(Writing by Brian Homewood; Editing by Tony Jimenez)
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