Still smarting from Sunday's 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, who beat Shamrock Rovers in extra time to win the FAI Cup on Sunday, had rarely managed to escape their own half but made it count when they 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.
What does it mean? European success a welcome distraction
Arsenal have taken just 13 points from 11 league games this season, which represents their lowest return at this stage of a top-flight campaign since 1981-82.
With that in mind, a shot at glory in Europe would serve as a welcome distraction from domestic toils.
As a seeded team in the draw for the next round, Arsenal will have realistic designs on extending their run in this competition beyond the last 32.
Eddie's ready to go
The fact Nketiah is now Arsenal's leading scorer might say more about the team's struggles than his own success – he does, after all, only have five goals to his name.
But given that Arsenal have netted just 10 times in the Premier League this term, Arteta must be considering adding to the solo start he has afforded the 21-year-old in the top flight.
Nketiah had five shots, created one chance and took his goal very well. Perhaps his withdrawal just past the hour mark was with the weekend's game in mind?
Pepe continues to toil
He scored in the reverse fixture, which Arsenal won 3-0, but was underwhelming in Ireland on Thursday.
It wasn't until the final 10 minutes that he provided anything of significance, laying on the assist for Balogun, but you expect more for £72million.
Key Opta Facts
- All three of Mohamed Elneny's goals for Arsenal have been scored in European competition, with two of those strikes coming outside the box.
- Arsenal have won all 11 games in which Eddie Nketiah has found the back of the net, with the young forward scoring 12 in total.
- The Gunners are the first team to have three English players aged 21 or younger (Folarin Balogun, Joe Willock and Nketiah) score in a major UEFA European match since Tottenham in 1982 versus Coleraine (Garry Brooke, Terry Gibson and Gary Mabbutt).
- Arsenal have scored twice as many goals in the Europa League this season (20 in six games) as they have in the Premier League (10 in 11).
Before the draw for the round of 32, which takes place on Monday, Arsenal host Burnley in the Premier League, while Dundalk's season is over.