The Gunners went behind when Martin Ellingsen curled a stunning effort past Bernd Leno from range midway through the first half.
Eddie Nketiah had a would-be leveller incorrectly chalked off for offside but a pair of own goals either side of half-time put them back in front.
Both were caused in large part by the excellent Joe Willock, with Kristoffer Haugen hooking into his own net while trying to hold off the Englishman, before substitute Sheriff Sinyan turned the same player’s cross into his own goal.
Bukayo Saka came off the bench to tee-up a third for Nicolas Pepe, who swept home smartly from the edge of the box, before Willock got his name on the scoresheet in Europe again with a powerful finish late on.
The result means Arsenal sit top of Group B, three points clear of the Norwegian side, and victory over the same opponents on matchday four would secure qualification for the last-32 with two games to spare.
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