Fischer scored with 11:20 remaining to lift Phoenix past the Nashville Predators 3-2 for the Coyotes' fifth straight home victory.
"Everybody can play hockey in this room," Fischer said. "It's a mental game, every sport, and when you start last you get down. Now we have a couple of wins and dug ourselves out of the hole, then you get breaks and when you get breaks you get more confident and more confident."
Oleg Saprykin and Yanic Perreault also scored and Mikael Tellqvist earned his first win for the Coyotes, who have won four of five to move within four points of Los Angeles for fourth place in the Pacific.
While fourth place in a five-team division generally isn't cause to celebrate, it would be a positive step for a team trying to overcome a 3-10-0 start.
"I was really thrilled with our effort from beginning to end tonight," Phoenix coach Wayne Gretzky said. "We played really disciplined hockey. It's probably our nicest win so far."
Ladislav Nagy gained control of a blocked shot low in the right faceoff circle and fed a quick pass in front of the crease to Fisher, who tapped the puck past goalie Chris Mason and into the open left side of the net for his fourth goal.
"My job is to go in front of the net there," Fischer said. "I knew he was going to shoot it and it just hit my stick and went in."
Mason had allowed long rebounds throughout the game, but the Coyotes were unable to take advantage until late in the second period.
Georges Laraque chipped the puck loose as Mason attempted to cover for a faceoff and Saprykin swooped in and poked the puck into the net to pull Phoenix within 2-1 at 17:41 of the second period.
Perreault tied the game 2-2 just 28 seconds into the third, firing a rebound from the low slot past Mason's glove for his team-leading eighth goal.
"I don't know where we'd be if we hadn't signed him," Gretzky said of Perreault. "He has given us a lift we've needed."
Shane Doan almost gave Phoenix the lead with 17:04 to play, bouncing a shot off the crossbar from the top of the right faceoff circle.
"It started in the second period and I think they just outworked us," Mason said. "They were hungrier than we were and it came down to being outworked."
Aided by three power plays, Phoenix spent most of the first period in the Nashville zone. The Coyotes outshot the Predators 12-6, but entered the intermission trailing 1-0.
Sullivan gave Nashville the lead 6:24 into the first when he took a pass from David Legwand and easily beat Tellqvist to cap a two-on-one break for a short-handed goal, his eighth.
Radulov made it 2-0 at 16:50 of the second period when he deflected Shea Weber's blast from the point over Tellqvist's shoulder for his seventh goal.
Tellqvist, making his first start since he was acquired from Toronto for Tyson Nash and a fourth-round draft pick on Nov. 28, made 19 saves.
"I just tried to go out there and have some fun," Tellqvist said. "It was only my second game of the year and I knew I was probably going to be rusty. After that second goal they got, we pretty much shut them down."
- Nashville has been outscored 34-18 in the third period. The minus-16 differential is the worst in the league. The Predators were outshot 16-3 for the period.
- Nashville is 13-1-3 when leading after two periods.
- Perrault, signed to a one-year free-agent contract on Oct. 29, has eight goals and four assists in only 13 games. Perrault played for Nashville last season, recording a career-best 57 points in 69 games.
- The Predators were playing the 600th game in franchise history. Nashville coach Barry Trotz also was coaching his 600th career game.
- The Coyotes have used four different goalies in 25 games.