Filip Chytil and Ryan Strome scored for the Rangers (5-5-1), who have won two consecutive games and three of four.
"It was a lot of cross plays side-to-side and a lot of screens, so I had to battle for that," Georgiev said. "But I think the guys helped me a lot with a lot of blocked shots. They played really hard from the beginning, and it was easier to play when we were leading."
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Viktor Arvidsson scored, and Juuse Saros made 28 saves for the Predators (8-4-2), whose point streak ended at six games (4-0-2).
"We were chasing the game," Nashville coach Peter Laviolette said. "I actually thought that we were probably at our best parts of the game defensively and fell down 2-0, and so [it was] kind of unfortunate the way that that happened. From there you're pressing.
"You've got to give them some credit; they played good defense. Their goaltender played well. We missed some opportunities, missed some shots, hit the post a few times and just couldn't seem to get it to fall tonight."
Chytil gave the Rangers a 1-0 lead at 16:05 of the first period, beating Saros with a wrist shot on a 2-on-1 rush after a turnover.