Nasreddine was coaching in his sixth game (1-4-1) after replacing John Hynes on Dec. 3.
"It felt really good, there were a lot of emotions. It's been an emotional 10 days," Nasreddine said. "I've been looking forward to this win. We've had some cracks at it, but finally we came through. It's a great day."
Darcy Kuemper made 31 saves for the Coyotes (19-12-4), who went 1-2-0 on a three-game homestand and are 8-8-1 in Arizona compared to 11-4-3 on the road.
"We had one goal. I didn't mind our game at all, but we didn't execute," Coyotes coach Rick Tocchet said. "We had chances to make a play and we didn't attack the net. You've got to make plays to score goals and we didn't."
After McLeod's initial shot was blocked by Coyotes defenseman Alex Goligoski, Palmieri collected the loose puck and scored top shelf from below the left circle to make it 2-1 at 11:34 of the third period. Blackwood started the rush with a stretch pass to Miles Wood at the Coyotes blue line.
"If you look at the performances everyone gave tonight, everyone was battling, working for each other," Blackwood said. "It was contagious and it's really nice to see, and I think everyone in here was really happy that we were able to get that one for [Nasreddine]."