Reyna, who is the son of former USMNT captain Claudio Reyna, scored in the ninth and 23rd minutes as Dortmund dominated their rivals.
Christoph Monschein and Aleksandar Jukic pulled goals back for Austria Vienna but they were no match for the scoring power of Reyna, Raphael Guerreiro, Immanuel Pherai, Jadon Sancho, Emre Can, Jude Bellingham, Taylan Duman, Marius Wolf, Thorgan Hazard and Nico Schulz.
An intricate exchange of passes between Reyna and Guerreiro led to Dortmund's first goal.
After knocking the ball about just outside the box, Guerreiro slipped the final ball beyond Austria Vienna's defence and Reyna converted with a right-footed shot past Patrick Pentz.
The 17-year-old added his second after 23 minutes when Manuel Akanji back-healed the ball into Reyna's path in the box and he hammered it home.
It looked like Austria Vienna were going to put up a fight when Monschein pulled one back on 33 minutes but two quick goals from Guerreiro and Pherai before the end of the first half dampened those hopes.
Both teams underwent full team substitutions at halftime but this change didn't make a dent in Dortmund's goal scoring abilities.
With help from Can, Sancho struck a right-footed shot from the centre of the box to the bottom left corner.
A lapse of concentration from Dortmund a minute later, however, saw Jukic hit a right-footed shot from outside the box past replacement keeper Marwin Hitz.
Sancho repaid Can on 65 minutes with the assist when he whipped a corner into the box and the Germany international headed it home.
A penalty conceded by Niels Hahn allowed Wolf to get in on the action on 76 minutes while Hazard added an eighth two minutes later.
New transfer Bellingham, who arrived from Birmingham City in July, added a ninth on 78 minutes.
Duman brought Dortmund into double figures in the 81st with a right-footed shot from the centre of the box.
Sancho got the assist again on 86 minutes when Schulz knocked it in from the left-hand side.