Following Saturday's disappointing 2-0 loss against Austria in Cardiff, John Toshack brought Motherwell's David Partridge, Cardiff's James Collins and Swansea's Sam Ricketts into a five-man backline, while Ryan Giggs partnered Craig Bellamy up front in the absence of John Hartson.
Austria boss Hans Krankl made just one change as Dietmar Kuhbauer came in for the suspended Emanuel Pogatetz.
The visitors started well and Bellamy broke clear after just two minutes, only to see his shot blocked by goalkeeper Helge Payer's legs, before the Austrian defence managed to hack clear follow-up efforts from Carl Robinson and the Celtic striker.
Bellamy then had a goal harshly disallowed for a slight push on Ernst Dospel, before Giggs saw two efforts blocked.
Wales finished the half on top but Bellamy and Mark Delaney both squandered good chances to give them an interval lead.
Toshack's side started the second half in a similar fashion and Giggs was surprised to see Payer make a superb reaction save to keep out his close-range effort from Ricketts' cross.
Austrian substitute Ivica Vastic, who scored the opener in Cardiff, then saw Danny Gabbidon block his close-range shot, before Andreas Ivanschitz smashed a shot against the Welsh bar.
Bellamy should have put Wales ahead 15 minutes from time when he surged into the box and rounded Payer, only for the keeper to somehow scramble back and block his effort.
Wales paid the price for their profligacy in front of goal three minutes from time when Coyne failed to deal with Aufhauser's tame 25-yarder and gifted Austria the points.