Goals from Eddie Nketiah and Mohamed Elneny in the opening 20 minutes appeared to put the visitors on course for an easy victory, but the Irish side got themselves back into the game in the 22nd minute thanks to an excellent goal from midfielder Jordan Flores.
Joe Willock but Arsenal back in control of proceedings in the 67th minute when he fired through Gary Rogers in the Dundalk goal to make it 3-1, before substitute Folarin Balogun made the points safe when he tucked away Nicolas Pepe's through ball 13 minutes later.
But the hosts plugged away and got a deserved second goal when Sean Hoare got in between two defenders to nod a great header past Runar Runarsson to complete the scoring.
The Gunners weren't at their best at any point in the game, but two very well-taken goals in the opening 18 minutes gave the Irishmen a considerable mountain to climb.
The visitors should really have had this game sewn up in the first half but took their foot off the gas after 20 minutes and could quite easily have found themselves level at 2-2 at the break.
Secondly, a number of fringe players failed to make the point to Mikel Arteta that they're worthy of more minutes in the Premier League.
6 -- It's difficult to come out of a game like this with a huge amount of credit but Arteta got the job done with a rotated squad that wasn't anywhere near its best.
Player ratings (1-10; 10 = best, players introduced after 70 minutes get no rating)
GK Runar Runarsson, 6 -- There was nothing the Iceland international could do to prevent Flores' effort from arrowing home but he looked a tad caught out by Hoares' late header.
DF Cedric Soares, 7 -- Somewhat unlucky to be booked midway through the first half for his part in what looked like a hard-but-fair duel for a loose ball. That said, the former Southampton man had a decent game and forced a couple of good saves from Rogers with efforts from distance.
DF Calum Chambers, 6 -- The 25-year-old was making his first appearance for 12 months and had to be alert to block a goal-bound effort in first-half stoppage time that would've drawn Dundalk level.
DF Shkodran Mustafi, 5 -- A scuffed clearance provided a glimpse of a half-chance for Dundalk, before the German failed to get close enough to Flores as the midfielder found space to fire home from distance.
DF Pablo Mari, 6 -- A couple of loose passes but it was to be expected with the Spaniard making just his second start of the season.
DF Ainsley Maitland-Niles, 6 -- Forced a good save from Rogers in the closing stages of the first half with a curling effort from distance but had a relatively lowkey evening.
MF Joe Willock, 6 -- The somewhat card-happy referee booked the youngster in the 30th minute for an accidental hand in the face of a Dundalk man, but the midfielder bagged himself a sixth Europa League goal for the Gunners when he fired home from close-range. Brought off for Miguel Azeez in the 83rd minute.
MF Mohamed Elneny, 7 -- Rifled home a brilliant goal from all of 30 yards to make the score 2-0 inside 20 minutes and was probably the steadiest of the Arsenal midfielders when out of possession. Switched for Dani Ceballos just after the hour.
MF Emile Smith Rowe, 6 -- Played his role in his side's second when he shifted inside and laid the ball on for Elneny to fire home, but the 20-year-old was always on the fringes of the game before being replaced by Ben Cottrell with 12 minutes to go.
MF Nicolas Pepe, 6 -- Failed to come out of a 50-50 with the ball and the resulting move led to Dundalk getting themselves back into the game. While the Ivorian struggled for large patches and looks short of confidence, he scrapes a "6" thanks to his assist for Arsenal's fourth.
FW Eddie Nketiah, 7 -- Opened the scoring after 11 minutes when he capitalised on a defensive error from the hosts, before delicately dinking the ball over the onrushing goalkeeper. Replaced by Balogun in the 62nd minute.
FW Folarin Balogun, 7 -- Showed good strength in the Dundalk box before providing the pass for Willock to finish for 3-1 and completed Arsenal's scoring soon after when he clinically slotted home.
MF Dani Ceballos, 6 -- Like many of his colleagues, the Real Madrid loanee had some sloppy moments in possession, but nothing to get into too much of a twist about.
MF Ben Cottrell, N/R -- Kept things tidy in the final 10 minutes or so.
MF Miguel Azeez, N/R -- Calm and composed on his Gunners debut.