Manchester City striker Jesus calmly curled past Heinz Lindner to open the scoring on 35 minutes.
Neymar, making his first start since February, doubled the lead midway through the second half, slotting in after a nice piece of skill.
Barcelona midfielder Coutinho added the third goal shortly afterwards.
He latched onto a through ball from former Liverpool team-mate Roberto Firmino before sliding home.
It could have been worse for Austria, Coutinho rattling the bar with a delicate effort after 76 minutes, and Firmino denied by a fine save in the closing moments.
Austria, who failed to qualify for Russia and have not competed at a World Cup since 1998, failed to pose much of a threat, though West Ham forward Marko Arnautovic did go close in the first half.
Brazil have not lost since June 2017, a run of 10 games, and have kept 16 clean sheets in 21 games since Tite took over in June 2016.
The five-time world champions, drawn in Group E, begin their World Cup campaign against Switzerland on Sunday, 17 June before facing Costa Rica and Serbia.
WHAT THE STARS ARE SAYINGâ€¦
“There is no fight to be Brazil’s national team top scorer. I think it’s just numbers. They are my idols, those who were here before me, and when it comes to idols, I will never be better than them. So I respect each one of them, Romario, Zico, Ronaldo, Pele… Because they are my idols. It’s just numbers. I’m happy to help my team, to score goals, but I don’t want to be better than them and neither will I be. Each one has their own history and knows their importance in the team. I’m very happy for the goals.”
*Brazil forwardÂ NeymarÂ on the chance of becoming his country’s top goalscorer
Â â€œIâ€™ve equalled Zidane and thatâ€™s something no one can take away from me. Trezeguet has three goals more and I want to catch him up and score as many as I can. On a personal level, itâ€™s an objective, an ambition.â€
*France forwardÂ Olivier GiroudÂ reveals his ambition to set a new scoring record with Les Bleus
“Individually, without a doubt (we are better). But football has developed considerably. Other countries have also come on leaps and bounds and their players have become much more technically refined. Comparing different generations doesn’t often get you anywhere. You simply have to keep up with the development of the sport, and in that sense, we’re ready. We are world champions, we have several players at the peak of their powers. We are looking forward to the tournament.”
*Speaking to DFB.de,Â Thomas MullerÂ feels world champions Germany have improved since their triumph at Brazil 2014
“England have a team with a lot of individual talent, you’ll have to watch out for several players. But the one who scores almost 30 goals every year is Harry Kane. He is the most dangerous.”
*Belgium goalkeeperÂ Thibaut CourtoisÂ is aware of the qualities that Group G rivals England will pose at the World Cup
“That it’s my last one makes it special and different. I try not to have the last World Cup in my head, but to face it as if I were the first – or what it is: a very nice challenge. I do not get tired from the goodbyes, I just try to enjoy every moment. I try to taste it because, after so much time, it is still exciting to live these moments.”
*Spain playmakerÂ Andres IniestaÂ is planning to make Russia 2018 a memorable moment in his illustrious career
â€œI am happy like all the Egyptians for qualifying for the World Cup after a 28-year wait. Our ambition is not to just participate in the tournament, we are working to qualify for the Round of 16.â€
*Egypt goalkeeperÂ Essam El-HadaryÂ is optimistic about the North African’s chance at the world finals
â€œNeymar is to me one of the best players in the world. Today, he is more mature and he has more experience, but he isnâ€™t going to win the World Cup on his own. Itâ€™s teams that win the World Cup. The greatest Brazil team of all-time was the one in 1970, with Tostao, Rivellino, Gerson and Pele all wearing the number 10 shirts for their clubs. In the 1970 World Cup, we spent more than six months together. Thatâ€™s why it worked.â€
*Brazil legendÂ PeleÂ believes the South Americans need to play as a team to win at Russia 2018