James van Riemsdyk, Jaromir Jagr, Max Talbot, Claude Giroux and Jakub Voracek all scored in the first period and Couturier's shorthanded goal 7 minutes into the second period made it 6-0 for the Flyers.
Wayne Simmonds and Matt Carle each tallied in the middle frame while Couturier closed out the Flyers' onslaught with another goal late in the final frame.
Ilya Bryzgalov stopped 33-of-35 shots for Philadelphia, improving to 10-5-0 in his career against Columbus.
Steve Mason let in seven of the Flyers' goals on 28 shots before exiting in the third period.
Allen York yielded two goals on five shots as Columbus dropped its 12th straight road game and fell to 2-11-1 overall.