Willian and Dani Ceballos were given their first starts in the Europa League by the Gunners, who had David Luiz back from injury and Bernd Leno between the sticks ahead of Runar Runarsson.
Molde were under early pressure as a goal-line clearance from Martin Bjornbak scooped a glancing effort from Eddie Nketiah away following a through ball from Nicolas Pepe.
A long clearance from Leno midway through the first half played in the visitors who then found Martin Ellingsen to crack the bottom-corner with a thumping strike outside the area.
Arsenal did have the ball in the back of the net when Nketiah got on the end of a cross from Pepe four minutes to halftime to turn home, but had the goal chalked off for offside.
The Gunners made their late dominance in the first half count after pressure play from Joe Willock saw Kristoffer Haugen direct Nketiah's surging ball from the right into his own net in added time.
Molde responded with a change at the start of the second half as Sheriff Sinyan replaced Stian Rode Gregersen whilst the hosts stayed unchanged.
The Gunners completed the turnaround midway in the second half when Sinyan helped a first-time ball from the right by Willock into his own net.
Mikel Arteta's men made the result more comfortable eight minutes later after another supply from out wide by Willock picked out Pepe, who slammed into the bottom-corner.
Arsenal made it four in the last three minutes when Willock ensured a fine evening's work with a top-corner finish from inside the area to cement top spot in Group B.