"It hasn't been a good feeling around here the past couple days," said winger Joffrey Lupul, who scored the shootout winner. "It's funny how even with an ugly, grind-it-out win like that, you come to the rink tomorrow feeling a lot better about yourselves."
The Leafs got shootout goals by Lupul and James van Riemsdyk and a couple of stops from Reimer, who made 34 saves.
The Leafs had the stronger play in regulation and the elimination of the kind of mistakes that led to 10 losses in their previous 13 games.
"It just goes to show that when we do execute what we plan on doing, things will fall into place for us."
Coach Randy Carlyle spent eight-plus hours at the rink Wednesday with the coaching staff on a day off for players devising what he hoped was a plan to turn the Leafs' fortunes around.
Presented at the morning skate was a blue print that included a harder forecheck and more aggressive defensive zone play.
For the most part, the Leafs followed that against Phoenix.
A strong forecheck was evident on Bodie's first goal of the season and first in a Leafs uniform, thanks to work from Holland and Jerry D'Amigo. The puck got out to defenseman Cody Franson at the point, and Bodie was in a good spot to put the rebound in on Mike Smith.
"[Forechecking is] something we've been stressing," Bodie said. "I think we did a good job of it on the goal. We got a good dump and we had two guys in on it right away and then the third guy joined. We were able to come out with it."
Toronto had tighter defense than it had displayed in a loss two days earlier to the Florida Panthers. That helped the lead stand up until Martin Hanzal scored 15:08 into the third.
Reimer, who started only because Carlyle said Jonathan Bernier was dealing with an unspecified "ailment," was satisfied with how his teammates contained the Coyotes and rebounded from a loss to Florida.
"We all make mistakes," Reimer said. "We sometimes don't show up in a way we want to. I think you're judged on how you respond. I thought we did a great job tonight. We really came collectively and everyone bought in."
Reimer turned aside attempts from Radim Vrbata and then Vermette in the shootout, but it was Smith's near-save on van Riemsdyk in the first round that caused a lengthy review.
Referee Paul Devorski assured Coyotes coach Dave Tippett that "110 percent" it was in the net, and video review found it inconclusive so the goal stood.
"You've got to take him for his word," Tippett said.
Devorski never signaled that it was a goal on the ice, which caused Smith some confusion.
"He came and whispered it in my ear like `it's a goal,' and he didn't really give a signal that it was," Smith said. "He made the call, he said he saw it go in. It's unfortunate, but that's the way it goes."
The NHL's statement on the play said only that "video review was inconclusive."
Despite their third straight loss, the Coyotes were satisfied with an improved performance.
"We definitely took some good things out of that game," said Smith, who made 26 saves. "It's not all bad. We did a lot of good things well in the third period there to give ourselves a chance to get a point. As long as we're in games, we're giving ourselves a chance to win hockey games, I think we'll be pleased with it."
The Leafs were pleased with the result as well as their improved play.
"I thought we were pretty strong for pretty much the full 60 and we did things the right way, so that was definitely an improvement," van Riemsdyk said. "We stayed patient, kept it simple and guys did their job, guys battled hard. It was a good two points."
Reimer was critical of his teammates after the loss to the Panthers, saying that some or all of the Leafs' players don't show up for the entire game.
"Obviously I was frustrated, but I try and always answer (with) the way I'm feeling -- in an honest way," Reimer said Thursday night. "Whether I'm frustrated or whether I'm happy, I try and answer objectively. I just answered how I thought I saw it."
Reimer felt relief after beating the Coyotes.
"Really proud of the way the guys worked," he said. "They put in an honest effort. It was just a good game all around. I thought we played solid for 60 minutes."
Gilbert Brule was in the lineup for the Coyotes, his first NHL appearance since May 15, 2012. Tippett said Brule, who played 12:39, was "flying" in his Phoenix debut. ... Defenseman Mark Fraser and Paul Ranger and tough guy Frazer McLaren were healthy scratches for the Leafs. ... Phoenix recalled defenseman Rostislav Klesla on Thursday morning to replace Zbynek Michalek, who returned to Arizona to undergo evaluation of a lower-body injury.