Franzen scored consecutive power-play goals 4 1/2 minutes apart early in the second period to break the game open.
Niklas Lidstrom and Danny Cleary scored and Franzen got his third goal on an empty-netter as the Red Wings won their second straight following an 0-5-1 skid.
Howard followed up a shutout in Detroit's win over Anaheim Saturday with another strong game, stopping 10 shots in the first period.
Colorado goalie Semyon Varlamov was yanked in the second period after allowing three scores on 16 shots. Jean-Sebastien Giguere came in and stopped 12-of-13 shots the rest of the way.
Gabriel Landeskog and Milan Hejduk scored for the Avalanche, who fell to 1-6-1 in their last eight meetings with Detroit.