Mattias Ekholm and Nick Bonino also scored, and P.K. Subban, Viktor Arvidsson and Roman Josi added two assists apiece as Nashville won for the seventh time in eight games. Pekka Rinne made 32 saves.
Mathieu Perreault scored twice and Tyler Myers had a goal and an assist for the Jets, who had won four straight.
Fiala scored the game's first goal at 3:31 of the opening period.
On a delayed penalty to Winnipeg, Fiala came on as the extra attacker. Subban faked a slap shot from the left point before sending a pass to Fiala in the lower part of the right faceoff circle. From there, he beat goalie Connor Hellebuyck between the pads with a spinning backhand.
Perreault tied it at 6:23 of the first.
With the Jets on a power play, Myers' slap shot from the center of the blue line hit Perreault standing just outside the crease, and the puck sailed over Rinne's left shoulder.
Johansen made it 2-1 just 26 seconds into the second with a wrist shot from the slot just underneath the crossbar.
After not scoring in the first 17 games of the season, Johansen has a goal in two of his last three. The goal was his 300th career NHL point.
Turris scored a power-play goal at 11:32 of the second with a slap shot from the left faceoff circle set up by a nice pass from Josi.
Nashville struck again on the power play at 19:02 of the second when Ekholm beat Hellebuyck with a slap shot from the high slot.
Ekholm has scored in four consecutive games, extending the best streak of his career.
Bonino scored at 9:16 of the third and Myers followed 1:23 later. Perreault scored his second of the night at 16:04.
