Germany-based Firmino fired home from 25 metres in the 83rd minute of the friendly to give Brazil a win they scarcely deserved after an unadventurous and often rough display.
David Luiz headed Brazil in front just after the hour and Austria levelled when Aleksandar Dragovic converted a penalty in the 75th minute, the first goal Brazil have conceded under Dunga's leadership. It was Austria's first defeat this year.
Dunga returned for a second stint in the job when he replaced Scolari immediately after the World Cup, which Brazil finished woefully, losing 7-1 to Germany in the semi-final and 3-0 to Netherlands in the third place match.