Dylan Strome also scored, and backup goalie Darcy Kuemper made 35 saves to help Arizona end a six-game losing streak vs. Columbus dating to 2014-15.
Fischer scored a goal in each period. He now leads the Coyotes with four goals in eight games.
"'Fish' worked really hard in the summer," Head Coach Rick Tocchet said. "He got his body fat down (and) he's a faster player ... We asked him to do middle drive, we asked him to slash. He does all the right things. He was rewarded tonight."
• The Coyotes fell behind, 1-0, just 31 seconds into the game when Pierre-Luc Dubois launched the puck from behind Arizona's goal off Coyotes forward Clayton Keller and into the net.
"That was just an unfortunate bounce," Kuemper said of the lone goal he allowed. "A terrible start for us, but what can you do? You've just got to stick with it. We got a big goal to answer back and make it 1-1, and then, from there, it looked like we got comfortable and got back to playing our game. The guys were battling hard and I was just trying to battle hard as well. When they're playing like that it makes it a lot easier, and I'm just trying to do my part. That was kind of our whole mind-set as a team tonight. Everyone just kind of did their job."