Having had the frame of their goal struck by Elena Linari early on, City – who lost 3-1 on aggregate to Atletico in the round of 32 last season – took a 13th-minute lead at the Academy Stadium when Janine Beckie fired into the top corner.
The visitors, with England and ex-City player Toni Duggan in their team, subsequently hit back via Corral in the 81st minute.
Miedema registered a first-half hat-trick to put Arsenal 3-0 up, netting in the 24th, 26th and 39th minutes, before adding her fourth seven minutes into the second half.
Kim Little boosted the advantage further with a penalty six minutes later, before goals for the hosts from Katerina Svitkova in the 71st minute and Mia Persson late on.
Glasgow City also produced an away victory, winning 2-0 at Brondby thanks to two own goals.
The Scots grabbed the lead in the opening minute of the contest as Sam Kerr’s shot was diverted in by defender Emilie Henriksen.
And goalkeeper Katrine Abel then fumbled a free-kick by Leanne Ross into her own net on the hour mark.
The away side had almost scored an own goal themselves seven minutes earlier, with Eilish McSorley’s header coming off the bar, and after the second goal Brondby hit the bar again through Nanna Christiansen.
Manchester City’s second leg will be played on October 30, with Arsenal and Glasgow City’s taking place 24 hours later.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies