Reilly Smith had the lone goal for Vegas, which has dropped three of four.
Trailing by a goal after one, Hartman and Fiala connected and turned a deficit into a lead just past the midpoint of the second period.
Hartman made it 1-1 at 11:27 of the second. From the left boards, Fiala passed to Hartman in the high slot.
''I was thinking shot,'' Hartman said. ''He was pretty tight on his gap, so I was able to step around him and kind of have a 1-on-1 with the goalie there.''
Fiala and Hartman teamed up again 57 seconds later to give Nashville a 2-1 lead. Nashville entered the Vegas zone on a 3-on-1. Fiala sent a nifty backhand pass from the right circle to Hartman at the left faceoff dot. Hartman did not get all of the puck with his one-timer, but he got enough to beat a sliding Subban high to the stick side.
''Today I was just thinking about playing the right way,'' Fiala said. ''Just simple game and not thinking about too much, scoring goals or whatever. If you stop thinking, sometimes it works, and today obviously it did.''
Fiala entered Tuesday with just three points in 11 games.
P.K. Subban, the older brother of the Vegas goaltender, picked up the secondary assist on the goal.
''I didn't think that we showed ourselves very well in the first period,'' Nashville coach Peter Laviolette said. ''But I thought the team and the lines and the players showed pretty well in the second and third.''
Smith scored the game's first goal at 17:14 of the first. With Vegas on a power play, an unchecked Smith skated to the left faceoff dot and snapped a wrist shot past Saros on the far side. Smith's goal was set up by a nice pass from Jonathan Marchessault along the right boards.
''They cashed in on our mistakes in the second period, and nobody stepped up after that,'' Marchessault said. ''(Subban) was awesome tonight and we weren't there for him.''
Making his fifth-straight start due to an injury to Pekka Rinne, Saros was sharp in the first, stopping 12 of 13 shots.
Jarnkrok gave Nashville a two-goal lead at 6:37 of the third. On another odd-man rush, Craig Smith sent a pass from the right side to Jarnkrok in the left circle, where he ripped a one-timer past Malcolm Subban, who finished with 24 saves.
''We made some bad choices on pinches that cost us a couple of goals tonight and gave them a lot of odd-man rushes,'' Vegas coach Gerard Gallant said. ''That's not what we usually do and it cost us tonight.''
With the Vegas goaltender pulled for an extra attacker with just over two minutes remaining in the third, Arvidsson was fouled from behind by Nick Holden on a breakaway and a goal was credited to the Swedish winger.
NOTES: Hartman had his first multi-goal game as a Predator. ... Nashville has allowed at least one power-play goal in its last four games. ... Predators D Matt Irwin played his first game of the season after being a healthy scratch for the first 11. ... Vegas has scored one power-play goal in three consecutive games.
Golden Knights: Visit St. Louis on Thursday.
Predators: Visit Tampa Bay on Thursday.
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