It was Neymar's 55th goal in a Brazil shirt, allowing him to draw level with Romario on his country's list of all-time leading scorers - only Pele and Ronaldo have more goals for their country.
Gabriel Jesus gave Brazil the lead after 36 minutes with a slick finish from a tight angle.
According to the bookmakers, Brazil are the favourites for the 2018 World Cup.
Brazil started the game in Vienna with a midfield formation that had only been on the pitch together for 60 minutes since Tite took over the national team.
In their 21 matches since Tite became head coach, Brazil have conceded just five times - keeping 16 clean sheets in the process.
However, Brazil will start their World Cup campaign against Switzerland (June 17), an adversary that will hardly attack them in a gung-ho fashion: as a matter of fact, the same could be said of the other Group E teams, Costa Rica and Serbia.
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Six minutes later, substitute Roberto Firmino set Philippe Coutinho clear down the left and he curled his shot wide of Lindner for the third.
Austria faces Brazil in an global friendly on Sunday at Ernst Happel Stadion in Vienna, Austria. Argentina had to wait a long time before booking their spot at the 2018 World Cup, but Brazil absolutely breezed through their qualification section.
Coutinho linked up with former team-mate Firmino for his goal. But Coutinho makes Brazil a more efficient team and certainly much more joyful to watch. They will also not take part in this summer's tournament having finished fourth in their qualification group - winning just four of their 10 matches.
Jesus' opening goal was offside, and whilst VAR will ensure this doesn't count once the tournament begins, it showed that Brazil finally now have a natural centre forward.
Not only does Neymar look healthy, he's making any concerns look foolish. Brazil is in red-hot form after their wins over Germany and Croatia.
Tite's side faced an Austria team that were coming off the back of a 2-1 victory over Germany last week, a result which extended their unbeaten run to eight games.