Vancouver had won four games in a row coming into the contest and the Red Wings had dropped four straight.
Howard surrendered a goal to Daniel Sedin with 5:48 to play in the opening period and then closed the door on the Canucks, who had scored 14 goals during their four-game winning streak.
Daniel Alfredsson tied it just past the midway point of the second period and Tomas Tatar supplied the game-winner with 1:02 to go in the middle stanza.
It was the first goal of the season for Tatar and the sixth of his career in 32 appearances scattered over three campaigns.
Roberto Luongo took the loss, allowing both goals on 30 shots.
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