Alfredsson, who played with the Senators for 17 seasons before leaving as a free agent in July, received a standing ovation before supplying an assist and an empty-net goal for the Red Wings.
Johan Franzen also scored as Detroit notched a fourth straight win.
Jonas Gustavsson stopped 30 shots.
Mika Zibanejad and Clarke MacArthur each scored for Ottawa, which dropped both ends of a two-game homestand.
Robin Lehner made 19 saves.