The Paris Saint-Germain defender broke the deadlock midway through the second half of the game at the Ernst Happel Stadion when he shrugged off the attention of Stefan Ilsanker to head home an Oscar corner.
The Austrians felt that Luiz had unfairly barged his marker out of the way but the centre-half felt that the goal was perfectly legitimate.
“I don’t think I fouled him,” the ex-Chelsea man told SporTV. “It’s always like this in the box, everyone’s always fighting for space.
“It’s tough. I’ve only pushed him a little and then I was able to score.”
Aleksandar Dragovic restored parity with a penalty but substitute Roberto Firmino struck in sensational style in the 83rd-minute minute to earn Brazil a sixth successive win under new coach Dunga.
“It’s a great start for this new cycle, but there’s a long road ahead of us,” David Luiz mused.
“It was a difficult match, against a strong team that went for every challenge. They gave us a lot of work to do.”
As well as winning six games on the bounce since Dunga replaced Luiz Felipe Scolari at the helm after the World Cup, the Selecao have also conceded just once during that streak.