Howard turned aside 19-of-20 shots in the first period and closed the door the rest of the way as the Red Wings rebounded from a shootout loss to Toronto in Wednesday's NHL Winter Classic at Michigan Stadium.
Rich Peverley scored a short-handed goal for Dallas, which fell to the Red Wings for the seventh time in nine meetings.
Dan Ellis was lifted after allowing three goals on 13 shots in the first period.
Kari Lehtonen stopped 12-of-14 the rest of the way.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut