Marc Janko fired the hosts into a 16th-minute lead but Marius Stankevicius levelled for the visitors after 66 minutes. However, Wallner stepped up to stroke in the winner from the spot after Franz Schiemer was brought down in the box.
The hosts opened the scoring with the first real chance of the game. Defender Schiemer found Janko and he surged into the area and drilled the ball into the top corner.
Nine minutes later Wallner's free-kick caused problems in the visitors' defence. Lithuania goalkeeper Zydrunas Karcemarskas cleared with his fists and Austria midfielder Yasin Pehlivan picked up the ball, but could not find the target. Wallner then attempted to lob Karcemarskas but the custodian saved well.
Lithuania's first opening of note came in first-half stoppage time, but after Schiemer had foiled Edgaras Cesnauskis' attempt to get in a shot, Veli Kavlak fired over.
Lithuania were more aggressive early in the second period and were rewarded after 66 minutes. A left-wing cross from Cesnauskis was converted by Stankevicius, who found the bottom corner from the centre of the area.
Stefan Maierhofer had a header cleared off the line before Schiemer was brought down in the box by Vidas Alunderis.
Wallner sent Karcemarskas the wrong way to restore Austria's lead, but there was still a moment of concern when Tomas Danilevicius had a shot blocked before the victory was sealed.