The tie was essentially over before half-time when Connor Tomlinson, Tra Lucas and Josh Boorn all found the back of the net in an 11-minute spell.
Tomlinson opened the scoring after Arthur Read's effort from the edge of the box was blocked and ran into the path of the striker, who made no mistake from six yards to give his side the lead with 36 minutes on the clock.
Three minutes later and his strike partner on the night Lucas doubled their advantage from the penalty spot, after he had been tripped when running through on goal. He took the resulting spot-kick and sent it straight down the middle, with the Arlesey keeper diving to his left.
Boorn made it three just before the half-time whistle when Read's well weighted pass for Tomlinson was just intercepted, but fell kindly for Boorn to strike first time, which he did – side footing it sumptuously from 25 yards into the bottom left corner.
The Town's prolific period all but killed the game off in the second half, with both teams struggling to create any real clear cut chances – although with 20 minutes to go, Lucas nearly turned provider as his low cross for Tomlinson was well cleared, with the striker almost certain to score had the ball reached him.
The Hatters pushed on for a fourth late on, and should have found it when Callum Nicholson fired wide from ten yards, but Tomlinson grabbed it as he snuck an effort past the keeper from a tight angle to secure Inigo Idiakez's side's spot in the next round of the competition.
Town: Isted (Parker 28), Neufville, Musonda ©, Panter, Byron (Greco 66), Beckwith, Boorn, Read, Kalonda, Lucas (Nicholson), Tomlinson.
On the bench: Parker, Stevens, Greco, Nicholson, Moloney.