Just over two minutes into the extra session, Minnesota's Jonas Brodin threw a low shot on net from the right point that a cutting Moulson redirected past Jimmy Howard to snap the Wild's two-game losing streak.
Gustav Nyquist tallied twice and Tomas Tatar recorded a goal and an assist for the Red Wings, who picked up a point to move into a tie with Toronto for seventh in the Eastern Conference. Washington, which was idle Sunday, sits one point back of Detroit.
Howard stopped 21 shots in the setback, which snapped Detroit's three-game win streak.
Celebrity Families of 2014 [PHOTOS]