For the second time in three Group B games, the Gunners had to come from behind after Martin Ellingsen beat Bernd Leno from 25 yards following a superb pass by former Manchester United reserve player Magnus Wolff Eikrem.
With no video assistant referee system in operation, Eddie Nketiah had what looked like a legal goal disallowed for offside before Arsenal equalised at the end of the first half.
Kristoffer Haugen put past his own keeper while trying to intercept Nketiah’s pass to Joe Willock before Sead Kolasinac blazed a great chance over the bar.
The Gunners took the lead when Molde substitute Sheriff Sinyan turned Willock’s pass across the six-yard area into his own net.
Substitute Bukayo Saka picked out Pepe to make it 3-1 before Willock added a late fourth goal, Arsenal three points clear at the top of the group with three games remaining.