Mehmet Ali's side weren't at all deterred by the torrential rain they faced in Wales and were off to a quick start through Catalin Cirjan.
The hosts almost restored parity instantly, but for a crucial intervention from Lino Sousa at the far post to deny them a certain equaliser from close range.
Nathan Butler-Oyedeji continued his impressive scoring streak to double the advantage five minutes before the break and sparked a spell of three goals that ultimately ended the game.
Charles Sagoe Jr made it three during added time, firing home from close range, before Catalin completed his brace with what was all but the last kick of the half after a threaded pass from Butler-Oyedeji.
Arsenal picked up the second half where we left off and Catalin almost secured his hat-trick shortly after the restart, but sent his effort over the bar from inside the penalty area.
Swansea scored a consolation goal in the closing stages, Corey Hurford finding the net from close range after Hubert Graczyk could only parry the initial effort on goal.