The Islanders preserved the one-goal lead by killing off back-to-back penalties in the third period. Varlamov made the biggest save during the kills at 6:51, when he used his stick to knock away a backdoor pass from Gustav Nyquist.
"When we had to kill, we killed," Varlamov said. "Guys blocked a lot of shots, especially from (Roman) Josi, he was shooting the whole night tonight. So, the PK was a key for us tonight. [Nashville] is a very skilled offensive team.
"Some pucks I saw and some pucks I didn't, a couple of times I thought I got lucky. They missed a few, like, opportunities. Luck was definitely on my side today."
Palmieri scored an empty-net goal at 18:41 for the 2-0 final.
The Predators outshot the Islanders 20-10 in the third period.
“I thought it was a good hockey game,” Nashville coach Andrew Brunette said. “They were a desperate team. I thought they defended their blue paint really well. I thought we did a lot of good things all through the ice, all through the game. Maybe we were a little bit sluggish early, and I thought we got going. We just couldn’t buy a goal late in the game.”
NOTES: It was New York's first win against Nashville since Oct. 28, 2017 (0-8-2 in previous 10 games). ... Dobson's goal was his 10th of the season. ... Barzal extended his point streak to four games (five assists).