In the extra session on a delayed call, Ruslan Salei sent a slap pass from the top of the left circle to the slot where Zetterberg redirected it between the pads of Ilya Bryzgalov for the win.
Nicklas Lidstrom and Dan Cleary each had a goal for the Red Wings, who have won four of their last five games. Jimmy Howard stopped 29 shots in the win.
Martin Hanzal and Keith Yandle each had a goal for the Coyotes, who have lost their past three games. Bryzgalov made 37 saves in a losing effort.