Howard was especially tough in the second period, stopping all 14 Coyotes shots he faced, while the Red Wings defenders clamped down late in the game, holding Phoenix to only six shots in the final stanza.
Phoenix goalie Ilya Bryzgalov let in three goals on 35 shots.
The Coyotes were playing without their regular-season scoring leader and captain Shane Doan, out with an unspecified upper-body injury sustained in the club's Game 3 victory.
Game 5 will be played Friday in Arizona.
2014: The Year in Music [PHOTOS]