Martin Hanzal scored twice to lead Phoenix 1, on Monday.
"We were gritty tonight. We found a way to get a win tonight on home ice when it was needed the most," Coyotes head coach Dave Tippett said. "We had a great effort from a lot of our guys tonight and that is going to be key down the stretch here."
Joey MacDonald made his first start since March 30 and absorbed the loss despite giving up just two goals on 22 shots.
Hanzal doubled the Coyotes' edge and netted the eventual deciding score on a power play less than seven minutes into the second by tipping in a Ray Whitney offering through bodies in the crease.
Detroit peppered Smith with 11 shots in the third, but had no answer. MacDonald was pulled for an extra skater with over a minute remaining and Hanzal put the clincher into an empty net inside of 30 seconds to play.
"We had some good scoring chances in the third there," said MacDonald. "We put some pressure on [Smith] and it was a 2-1 game. We just have to have a little more I think."
Gordon put the hosts on the board at 7:22 of the opening period in a short- handed situation. He managed to elude a pair of Detroit players to snag an errant pass off the left boards, skate in and deke MacDonald before sliding a shot home at the right post.
Detroit won three of four games in the season series...Hanzal posted his first multi-goal effort since October 23...Whitney picked up a pair of assists...Prior to the game, Phoenix recalled defenseman Chris Summers from Portland of the AHL...The Coyotes travel to Dallas on Tuesday...The Wings, who finished 2-2-1 on their sojourn, return home to open up a six-game homestand by welcoming Edmonton on Wednesday.