Stone fired a slap shot from the right point that went through teammate Martin Hanzal's screen and caromed in off the far goal post. It came 2 seconds after a Coyotes power play ended. Stephen Weiss, who received a hooking penalty with 6:49 left, had just come out of the penalty box.
"Got an opening and a chance to shoot," Stone said. "(Mike) Ribeiro mad a great pass, and I got a screen in front from Marty Hanzal.
"To respond the way we did after two ugly ones is the way to go."
Vermette added an empty-net goal in the last minute.
"I didn't think we played very well," Red Wings right wing Daniel Cleary said. "It wasn't a very good game defensively, and we didn't spend enough time in their zone.
"That's two games in a row that we haven't looked like us."
Detroit lost 4-1 at Boston on Saturday night.
The Coyotes also dominated in the faceoff circle, winning 46 of 70 draws.
"Our faceoffs were really strong," Phoenix coach Dave Tippett said. "There's always little things that you want to tweak."
Andersson, Detroit's third-line center, addressed the faceoff situation.
"They are known to be good faceoff guys, a couple of them, but we have to be better than we were tonight," he said. "I don't know what the stats are, but that's how I felt.
"We knew those two guys (Hanzal, Vermette) are real good on faceoffs. We have to dig in better next time."
Andersson put a rebound over Smith's shoulder 5:07 into the second period to tie it 1-1. It was the first goal of the season for the Red Wings' third line, which also features Cleary and Todd Bertuzzi.
Ericsson's floating shot from the right point found its way into the net at 6:00.
But Boedker made it 2-2 by scooping up a loose puck and putting it in just 1:04 later.
Morris opened the scoring just 2:21 in when his slap shot from the right point got past Howard after Vermette beat Stephen Weiss cleanly on a faceoff.
Phoenix D Rostislav Klesla made his season debut. He opened the season on the injured list because of a concussion and whiplash sustained during the preseason. ... Detroit LW Patrick Eaves, on long-term injured reserve with a sprained left knee ligament and sprained left ankle, said he should be available to play on Oct. 26. ... Phoenix RW David Moss is from Detroit and played at the University of Michigan. ... Red Wings RW Daniel Cleary played with the Coyotes in 2003-04.
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DETROIT, MI - OCTOBER 10: Derek Morris #53 of the Phoenix Coyotes celebrates his first period goal with Keith...