"It's nice to get that one under the belt," Fischer said. "That's my game, just getting to the net ... I didn't think about scoring today, I just thought about playing. When I saw it go in, I was just filled with emotion."
Fischer is the 11th Coyotes player to score a goal in his NHL debut.
The Coyotes selected Fischer 32nd overall in the 2015 NHL Draft, and recalled him from the American Hockey League on Friday. While playing in the AHL this season, Fischer notched 16 goals and 16 assists in 31 games.
Fischer's parents flew to Arizona from Chicago on Friday and were at Gila River Arena to witness their youngest child's first NHL game and goal.
Fischer played 10:57, including 1:33 of penalty killing, and delivered one hit.
"It's nice to put up the goals but I take a lot of pride in ... playing that full team game, that full 200-foot game," Fischer said. "... As the game went on, I felt more and more comfortable. Obviously first period, jitters are always an issue. Maybe gripping your stick a little tight, but to get my first one out of the way and to get more comfortable as the game went on, I think it just grows my confidence and I'm excited to see where it can take me."