Panama goalkeeper Jaime de Gracia saved two penalties to keep his side in the game, despite them going down to nine men as two players were given red cards.
As the rain tumbled down at Wellington Regional Stadium, Panama searched for an equaliser but it wasn't forthcoming in a game that included some spiteful moments between both sides.
Panama's heavy tackling wasn't appreciated by the Austrians who tried to employ their technical passing game, despite the wet conditions.
The result has put Austria in a good position to get out of the group stages but they still need to meet tournament favourites Argentina in their final pool game.
Austria 2 (Chin Hormechea 45+1 og, Valentin Grubeck 51) Panama 1 (Fidel Escobar 38) halftime: 1-1