Kreider scored 34 seconds later on a 2-on-0 with Zibanejad to tie it at 1-1.
The Rangers thought they took the lead at 2:20 of the second period, but the puck off Panarin's shot went off Ekholm, the left post and the back of Saros' left leg before stopping on the goal line. Saros covered up the puck and the play was reviewed, determining the puck didn't cross the line.
"That one was dancing on our goal line," Ekholm said.
Nashville regained the lead 2-1 on Josi's wrist shot from the right circle at 11:16 of the second.
Ekholm made it 3-1 with a breakaway goal at 15:23 of the second, 12 seconds after he exited the penalty box.
Nick Bonino forced a turnover in the Predators zone, got the puck, and lifted it up and out to Ekholm, springing him on the breakaway. Ekholm scored with a forehand shot.
"I got out there and we got the puck and I was screaming at Bonino, and he made a terrific play," Ekholm said. "I knew I had the legs and they kind of didn't. Somewhere in there I was starting to think that maybe I can get a break here, and lucky enough I did."
Ekholm wasn't certain he would play because of an illness that kept him in bed for the past four days. He woke up Monday morning at home in Nashville feeling better and was able to fly to New York and arrive by 1 p.m.
"I was hoping but yesterday morning I thought for sure I wasn't going to play because I still had a high fever and all that," Ekholm said. "It kind of went away midday and then I got hopeful at night. I'm happy it turned out the way it did."
Panarin scored to make it 3-2 with 2:42 remaining in the third period, extended his goal-scoring streak to five games, tying his career long streak.