But strikes by Lia Waelti and new signing Mariona Caldentey inside 40 minutes gave Jonas Eidevall’s side the lead prior to the break.
Beth Mead and Frida Maanum then put the tie beyond Hacken’s reach as Arsenal ran out 4-0 winners.
Manchester City went into their home leg with a comfortable 5-0 advantage after a dominant first-leg display in Paris last week.
A goal after two minutes by England striker Chloe Kelly effectively put an end to any hopes of an unlikely Paris FC comeback, before Khadija Shaw scored just after the half-hour and hour marks to seal a 3-0 win.
Real Madrid won 3-1 at home to Sporting Lisbon, with a brace either side of half-time by Sandie Toletti and a goal in second-half stoppage time from Alba Redondo easing the Spaniards to a three-goal winning margin over both legs.
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