Tony Duggan added another straight from kick-off as he ran through the defence like butter while they increased the lead to 18-0 in as many minutes when Mark Dalle Cort broke through.
The visitors could have gone ahead in the seventh minute after Hugo Colace dinked a ball over Andre Bikey for Goran Lovre, but Leon Cort came racing back to clear the danger.
Pulis believes he has a good knowledge of players and signed the likes of Ryan Shawcross and Richard Cresswell during the summer, while Danny Pugh and Leon Cort arrived on loan early in the season.
He spent a few years as a teacher before deciding to pursue a career as a tattoo artist with an apprenticeship at Cort's Royal Ink Tattoo Studio in Patchogue, New York.
Without their captain the Gunners lack their usual midfield zest and Burnley equalized six minutes after the half-time interval when David Nugent latched on to Leon Cort's header and directed the ball over goalkeeper Manuel Almunia.
But they have problems up front with John Hartson ruled out until March, Carl Cort struggling with a hamstring injury and Marcus Gayle about to depart on international duty.