Fiala took a pass from Craig Smith and deked to his backhand, lifting a shot just off the glove of goalie Connor Hellebuyck for his third goal of the playoffs and his second of the series.
The teams next head to Winnipeg for Game 3 on Tuesday night.
The Jets forced extra hockey with an extra attacker. Mark Scheifele scored his second goal of the game at 18:55 of the third period when he roofed his NHL-high eighth goal of the playoffs and fourth marker of the series.
Ryan Johansen's second goal of the contest gave Nashville a 4-3 edge at 5:45 of the third period, answering Brandon Tanev's equalizer 34 seconds earlier off a Predators turnover.
In most ways, Winnipeg played a far better game than it did on Friday night, when it was outshot 48-19. The Jets carried play for most of the third period and finished the evening with a 50-41 advantage in shots on goal.
But Hellebuyck, who was easily the best player on the ice in Game 1, was merely human in this one. He made 36 saves, although he played better as the night progressed.
Pekka Rinne, who was pulled from Game 1 following the second period after permitting three goals on 16 shots, bounced back with 46 saves for Nashville.
Johansen put Nashville ahead just 27 seconds into the game with his first goal, skating into the slot and wiring a wrister just inside the right post off a Filip Forsberg feed.
Winnipeg responded with two goals in a 29-second span late in the opening period. Dustin Byfuglien bagged his first playoff goal at 12:47 with a sharp-angle wrister from the right circle through Rinne's pads, and Scheifele tallied on the power play.
The Predators answered with two second-period markers. P.K. Subban bombed a point shot off the left post on the power play at 5:04 for his first goal of the postseason, and Arvidsson registered his third at 18:41 on a slapper from the right faceoff dot.
Forsberg wound up with three assists while Arvidsson had two. Scheifele had a three-point game. Byfuglien and Subban each had a goal and an assist.
--Field Level Media
Winnipeg | Nashville | |
Mark Scheifele 3 | Points | Viktor Arvidsson 3 |
Mark Scheifele 2 | Goals | Ryan Johansen 2 |
Mark Scheifele 1 | Assists | Filip Forsberg 3 |
Mark Scheifele 1 | Power Play Goals | P.K. Subban 1 |
N/A | Short Handed Goals | N/A |
Connor Hellebuyck .878 | Save Percentage | Pekka Rinne .920 |
Connor Hellebuyck 36 | Saves | Pekka Rinne 46 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Winnipeg | 50 | 4 | 1-4 | 3-4 | 10 | 36 |
Nashville | 41 | 5 | 1-4 | 3-4 | 10 | 57 |