"Fids did a great job of winning [the faceoff]," Winnik said. "I managed to cycle off of it and I happened to beat the guy to the net."
Brian Rolston's wild, spinning shot from the blue line eluded Ilya Bryzgalov with 4:44 to go for his second goal of the night to pull the Devils to 4-3.
"We allowed them to come back in the game and we just kind of stepped on it at the end," Winnik said.
Matthew Lombardi and Peter Mueller also scored for the Coyotes, who snapped a four-game home losing streak. Phoenix won for the second time in its past seven games (2-3-2) despite being outshot 34-19, including 15-1 in the second period.
"We still don't think we've played our best game," Phoenix's Shane Doan said. "We know we can be better than that but we found a way to win."
Travis Zajac also scored for the Devils, who lost for only the sixth time since Nov. 21 (18-6-0).
"In the second period we didn't execute well with the puck and couldn't catch up to the pace of the game," Tippett said. "That was a wake up call for us. This last four, five games is the first real adversity we've gone through this year. It's going to build character."
"It was all one play," Rolston said. "They got the backdoor goal and they got the power play out of it and scored. They were resilient tonight."
Lombardi gave the Coyotes a 1-0 lead when he redirected Keith Yandle's pass from the top of the right faceoff circle between Brodeur's pads at 13:16 of the first.
Mueller stole the puck off the stick of Devils defensemen Colin White just inside the Phoenix zone and outraced the defense down the ice before beating Brodeur with a wrist shot to make it 2-0 with 30.4 seconds to go in the first.
"Confidence is earned," Tippett said. "The goal he scored tonight was an outstanding individual effort. We've been looking for that all year."
Rolston took a long outlet pass from Rod Pelley at the Coyotes' blue line, skated in and beat Bryzgalov with a wrister over the goalie's blocker to cut the lead to 2-1 at 9:21 of the second period.
"I felt like I had a bounce back game [Tuesday] against the Rangers," said Rolston, who ended a nine-game scoring drought. "I think that's what I needed. Even though I didn't score I got some opportunities and got my confidence back."
Zajac tied it at 14:06 on a sharp shot from the high slot after Zach Parise broke up a clearing attempt at the top of the right faceoff circle.
"In the first period they had the two goals and we talked about what they were doing well," said Devils coach Jacques Lemaire. "In the second period we came back strong."
Coyotes defenseman Ed Jovanovski served the second game of his two-game suspension for elbowing the Islanders' John Tavares in the chin Saturday. ... Zajac has three goals in four assists in his last four games. ... Mueller's goal was his second in three games after going two months without one. ... Parise's assist was his 300th career point.
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GLENDALE, AZ - JANUARY 14: Martin Brodeur #30 of the New Jersey Devils stretches before a game against the...