Mikel Arteta made 10 changes to the side that lost 1-0 at home to Leicester City last weekend and they were kept at bay for 42 minutes by an effective Dundalk rearguard until Eddie Nketiah pounced on a goalkeeping error.
Joe Willock doubled the lead before half-time and Nicolas Pepe's super strike put the Gunners firmly in control, allowing them to ease through the closing stages with one eye on the weekend trip to Manchester United.
Patrick McEleney tested Alex Runarsson with the first effort of the match as Dundalk showed they were prepared to work the ball forward rather than simply clear their lines.
Arsenal unsurprisingly controlled possession yet found it difficult to pick its way through a packed visiting defence, but Nketiah got the breakthrough three minutes before half-time, turning home from point-blank range after goalkeeper Gary Rogers made a mess of an attempted punch.
Dundalk was punished further barely 90 seconds later, Willock firing high into the net after Nketiah and Pepe led a swift break in the visitor's half.
Any faint thoughts of a comeback were quashed just a minute after the restart, Pepe taking a clever touch and curling a fine effort into the top-right corner from the edge of the Dundalk box.
Nketiah just failed to prod a cross beyond Rogers from Cedric Soares' cross, and the lively Reiss Nelson teed up Kieran Tierney to blast over, but the fight was gone from the Irish champion.