It was Manuel Pascali this time who was called upon to make a last-ditch, goal-saving block to prevent Colin Healy's shot finding the target from eight yards.
Falkirk had a clear opportunity to reduce the deficit just after the hour mark, when Scotland squad member Paul Dixon failed to cut out Colin Healy's pass to Vitor Lima, who picked out Enoch Showunmi.
The decisive goal came in the 78th minute when Priskin ran on to a through ball from ColinHealy and took one touch before drilling his strike into the bottom corner beyond Gunners goalkeeper Wojciech Szczesny.