Kronwall, positioned in the slot, one-timed Henrik Zetterberg's pass through a screen and past Ilya Bryzgalov into the left corner of the net for the win.
Detroit's Pavel Datsyuk scored the goal that sent the game into overtime.
The Red Wings got 25 saves from goalie Jimmy Howard to end a two-game losing streak, while Bryzgalov turned aside 31 shots for the Coyotes.
The Phoenix goal came from Martin Hanzal.
2014: The Year in Music [PHOTOS]