The visitors struck first just after the 20-minute mark when Martin Ellingsen picked up the ball on the right flank, cut inside and blasted a lovely left-footed shot past Bernd Leno to give Molde the early lead.
A well-organised Molde defence kept Arsenal largely at bay for the rest of the first half, but the Gunners got back on level terms before the break when Kristoffer Haugen redirected a cross into his own net to make it 1-1.
Sead Kolasinac wasted a golden opportunity to put Arsenal ahead, firing over in front of a wide open net after the ball fell to him at the far post and the match stayed level.
Arsenal were in front soon after, though, thanks to another Molde own goal when Sheriff Sinyan shinned the ball in and then they doubled their lead in the 69th minute with a clinical finish from Pepe to put further pressure on the visiting side.
Joe Willock scored Arsenal's fourth, picking up a through ball from Pepe and firing home from close range after a clever first touch left him with just the goalkeeper to beat.
Willock, who hasn't played in the Premier League at all this season, was called in for praise by Arsenal boss Mikel Arteta and the manager said the youngster has his trust.
"The thing is we have a really big squad at the moment. I said to Joe that I really trust him," Arteta said. "This is a competition we are not treating to give players a chance, it's as competition we take really seriously, we want to play players that are in the best possible shape to give us the result we need and Joe is one of them.
"I think he was really strong in his performance. I think the way he is approaching every opportunity shows how mature he is."
Next up for Arteta's side is a Premier League match at home against Aston Villa on Nov. 8 ahead of the next international break.
ESPN writer James Olley contributed to this report.