Joe Allen’s superb strike and a Kevin Wimmer own goal twice gave Wales the lead, but they were pegged each time by Stoke forward Marko Arnautovic.
Allen had not scored for his country until his 32nd international appearance against Moldova last month.
But he made it two in as many games with a spectacular 22nd-minute volley after Chris Gunter had nodded the ball into his path.
Wimmer’s unfortunate moment came on the stroke of half-time after goalkeeper Robert Almer had pushed James Chester’s close-range effort into his path as he lay on the floor.
In between, Arnautovic struck with a smart header and then levelled three minutes after the restart when Wales defence were guilty of some careless defending.
Austria’s miserable Euro 2016 campaign had been in direct contrast to that of semi-finalists Wales.
But they were on a 10-game winning streak in European Championship and World Cup qualifiers and had not lost a competitive home fixture since Germany beat them in 2012.
Meanwhile, Southampton’s Dusan Tadic was Moldova’s chief tormentor as the Republic of Ireland’s second opponents in this week’s Group D double-header slumped to a 0-3 defeat at home to Serbia.
Ireland visit the Stadionul Zimbru in Chisinau on Sunday, where the Serbians cruised to victory last night, having got the bulk of the job done in the first half.
Tadic pounced on a loose touch in the Moldovan defence to race clear and set up Hamburg midfielder Filip Kostic for an easy finish to put Serbia in front after 19 minutes.
The visitors doubled their lead on 37 minutes with Tadic once more the provider, his cross following a corner allowing captain Branislav Ivanovi to score with a header at the back post.
The Moldovans hadn’t yet managed a shot on target, though Cojocari sporadically threatened, drilling just wide on 56.
However, on the hour, Tadic wrapped up the points, slotting home inside the box after being set up by Aleksandar Katai.