Mark Jankowski also scored for Nashville, which snapped a two-game losing streak.
Filip Chytil scored and Jaroslav Halak made 16 saves for the Rangers, who lost for the fourth time in five games.
Pärssinen put Nashville in front 4:58 into the opening period, driving down the right side before beating Halak high to the far side.
Making his NHL debut after being recalled earlier in the day from Milwaukee of the AHL, Pärssinen's goal came on his first shot on goal.
Jankowski scored 8:37 into the second. He got his second of the season after Roman Josi intercepted an attempted clear by the Rangers before finding Jankowski all alone in front.
Chytil halved the Nashville lead at 11:56, scoring from the slot off of a smooth pass by Adam Fox from behind the Predators net.
With the assist, Fox extended his point-scoring streak to five games.
The Rangers could not find the equalizer though, despite a third-period double minor penalty for high sticking assessed to Nashville defenseman Jeremy Lauzon and pulling Halak for an extra attacker.
LATE PICK PAYS OFF
The Predators selected Pärssinen in the seventh round of the 2019 draft. He is playing his first season in North America. He had two goals and seven assists in 10 games for Milwaukee prior to his promotion.
RANGERS STREAKS SNAPPED
In the loss, New York’s Mika Zibanejad and Chris Kreider had their seven-game point streaks stopped. Over the previous seven games, Zibanejad had 10 points (five goals, five assists) and Kreider had nine (four goals, five assists).
It was Nashville’s first home game in two weeks. A quick one-game trip to Detroit to play the Red Wings on Nov. 23 will be the only time the Predators will leave Music City through the end of the month.
Rangers: Host the Arizona Coyotes on Sunday.
Predators: Host the Minnesota Wild on Tuesday.
AP NHL: https://apnews.com/hub/nhl and https://twitter.com/AP_Sports
Jim Diamond, The Associated Press