The Red Wings, who are in a fight just to earn a spot in the playoffs, bounced back from a 6-0 thrashing at the hands of the New York Islanders in what was the finale of a five-game road trip.
Howard, who was removed from the loss to the Islanders after giving up three goals, was beaten by Tom Kostopoulos 7:17 into the third.
Henrik Zetterberg then gave the Red Wings some insurance with 5:20 to play.
Cam Ward allowed three goals on 35 shots to take the loss. Carolina's 14 victories are the fewest in the NHL this season. The Carolina franchise has lost 14 consecutive games in Detroit dating to Nov. 14, 1989 -- when the team was known as the Hartford Whalers.