Arsenal Women already had a comfortable lead ahead of the second leg of their second round tie after beating Slavia Prague 3-0 at home last week.
They duly finished the job in style away from home, running out 4-0 winners as Miedema scored a hat-trick.
The third of those goals was the striker’s 100th for Arsenal and she has reached that tally in just 110 games.
Miedema opened the scoring for Arsenal on the hour mark and within 12 minutes she had completed her hat-trick.
Kim Little rounded off the rout in the 75th minute by scoring a penalty and the Gunners can now look forward to the group stages of the WCL.
The club have made a flying start to life under head coach Jonas Eidevall; beating reigning Women’s Super League champions Chelsea in their season opener at Emirates Stadium last weekend too.