Profligacy plagued the Gunners during the first half at Linkoping Arena, but the floodgates opened in the second 45 as Caitlin Foord, Lina Hurtig and Stina Blackstenius breached the hosts' backline.
Jonas Eidevall's side squandered a magnificent chance to take the lead in the seventh minute as the normally-reliable Kim Little was denied from the penalty spot by Cajsa Andersson, who also pushed a Lotte Wubben-Moy header onto the post in the 28th minute.
However, Little soon made amends eight minutes into the second half, showcasing delicate footwork to get to the byline inside the penalty area and crossing for Foord to nod in the opener at the back post.
Arsenal initially struggled to convert their dominance into more goals, as Andersson was called upon to push Frida Maanum's effort onto the post in the 64th minute, but the Linkoping goalkeeper soon went from hero to zero.
With 81 minutes gone, Andersson came to claim a free kick floated into the box by Katie McCabe, but she was beaten to the ball by Hurtig, who sent a deft header into the bottom corner with her back to goal.
Any lingering doubts were extinguished in the 90th minute, as Foord squared for Blackstenius to complete the rout against her old club, calmly netting through the legs of Andersson from close range.
Eidevall's team will now meet either Paris FC or Ukrainian outfit Kryvbas Kryvyi Rih on Saturday for a spot in the second qualifying round.