Howard faced 16 shots in the final frame, and was dented by Paul Stastny with 1:30 remaining as the Avs pulled to within a goal.
They then pulled goalie Jean-Sebastien Giguere to add a sixth attacker, but Howard held firm down the stretch to secure Detroit's fourth win in six contests.
Niklas Kronwall was credited with the game-winning goal late in the second period when his wide shot took a fortuitous bounce off the boards, glanced off Giguere and went into the net.
Johan Franzen also tallied for the Red Wings.
Giguere finished with 31 saves for Colorado, which fell to 0-3-3 in its last six road games.