Still smarting from Monday's (AEDT) 2-0 loss to Tottenham in the north London derby, the Gunners made it six wins on the bounce in a major European competition for the first time since 2005.
Arteta, who unsurprisingly made sweeping changes from the weekend for what amounted to a dead rubber, saw Eddie Nketiah break the deadlock before Mohamed Elneny's sweet strike put his side firmly in the ascendancy.
It was not entirely one-way traffic, though, and Jordan Flores thrashed a powerful shot beyond Runar Alex Runarsson to give Dundalk a moment to savour.
However, second-half goals from Joe Willock and substitute Folarin Balogun put the game to bed as Arsenal made it a club-record nine consecutive away games unbeaten in Europe, ensuring Sean Hoare's header was merely a consolation.
Nketiah, who had already been involved in two promising situations, opened the scoring 12 minutes in when he blocked an attempted Andrew Boyle clearance before lifting a neat finish over the onrushing Gary Rogers to become Arsenal's top scorer in all competitions this season.
The second goal arrived soon after and it was a stunner from the right boot of Elneny, who picked out the top-right corner from outside the box.
Dundalk, which beat Shamrock Rovers in extra time to win the FAI Cup on Monday, had rarely managed to escape its own half but made it count when it did.
Flores received a pass from Michael Duffy before driving his attempt across Runarsson and into the back of the net, despite the Iceland international having got fingertips on it.
A crucial block from Calum Chambers denied Darragh Leahy an unlikely leveller on the stroke of half-time, but Arsenal finished the job in the second half.
Willock kept his cool with possession inside the area and drilled a low shot underneath Rogers, with Balogun similarly level-headed after coming off the bench to convert from close range.
Hoare's flicked header restored a sense of pride for Dundalk, who nonetheless finish bottom of the group and without a point.