The Paris Saint-Germain forward scored the second of the Selecao's three goals on his first start for club or country since February 25.
After spending 14 weeks on the sidelines, Neymar has now netted in back-to-back matches for Brazil and appears in perfect shape for their Russia 2018 opener against Switzerland in a week's time.
Both teams then squandered good openings, as Marko Arnautovic blazed over from a promising position and Coutinho could not quite curl the ball past Lindner.
In an open first half, Paulinho was the next to be denied after Neymar was taken down inside the penalty box.
Brazil did take the lead nine minutes before the interval, however, through Jesus's impressive curled finish after a corner was not fully cleared.
Coutinho and Arnautovic both had shots saved at the end of the opening 45 minutes, and the Barcelona ace came close to finding a way through on the hour mark from the next big opening.
Lindner kept that effort out, but there was no stopping Neymar a minute or so later as he finished coolly after being picked out by Willian.
The visitors really stepped things up from that point as, after Paulinho had a shot saved, Coutinho exchanged passes with substitute Roberto Firmino and rounded Lindner.
Coutinho then struck the crossbar in search of his second and Firmino became the latest player to be denied by an overworked Lindner following some nice interplay.
Austria were outclassed at times in the second half but they nearly pulled one back through Stefan Hierlander, whose bullet strike was turned over the bar by Alisson.
Neymar was taken off inside the final 10 minutes to a strong ovation from the Austrian supporters, and the man who replaced him in Douglas Costa nearly added a fourth for his side, seeing his effort parried aside.
AUSTRIA (3-4-3): Lindner; Dragovic (Danso 70'), Prodl, Hinteregger; Lainer, Baumgartlinger, Grillitsch (Zulj 66'), Alaba; Schopf (Hierlander 58'), Schlager (Burgstaller 58'), Arnautovic
BRAZIL (4-3-3): Alisson; Danilo, Thiago Silva (Marquinhos 60'), Miranda, Marcelo (Filipe Luis 67'); Coutinho (Taison 76'), Casemiro (Fernandinho 61'), Paulinho; Neymar (Douglas Costa 84'), Gabriel Jesus (Firmino 67'), Willian