After a scoreless opening period, Jones gave the Predators a 1-0 lead at 1:03 of the second.
With Nashville on a power play, Shea Weber had the puck at the right point. Weber found David Legwand on the right boards, and Legwand slid a cross-ice pass to Jones at the top of the left circle. Jones took the puck and beat Nabokov on the short side with a slap shot.
"The seam was there for a couple of seconds, and I was hoping that Leggy saw me," Jones said. "He's got good vision, so he did."
The 19-year-old defenseman was put on the left side of Nashville's top defensive pairing alongside Weber. He took that spot after Roman Josi sustained a concussion just over a week earlier in a game at Colorado.
Nielsen tied it at 12:39 of the second after Kyle Okposo found him with a pass as Nielsen came through the high slot unchecked. He snapped a wrist shot past Rinne.
Less than three minutes later, Tavares gave the Islanders a 2-1 lead when he banked in a shot from below the goal line off of Rinne's right pad.
Hornqvist sent the teams into the second intermission tied at 2 after his shot from the right circle beat Nabokov with 53 seconds remaining in the period.
"It was a huge goal," Nashville coach Barry Trotz said. "He sort of willed that puck in the net. You can say what you want; good goal, bad goal, whatever. I really believe that it was that extra effort that helped us get that goal."
It was Hornqvist's first of the season.
"That was a big goal for them, obviously, under a minute left to go in the second period," Islanders coach Jack Capuano said.
Ellis netted the winning goal 3:23 into the third when his slap shot from just inside the blue line on the right side beat Nabokov on the stick side.
"Just put the puck on net. I think that is what we have been doing lately, but we weren't getting bounces," Ellis said. "Tonight we did get a few, and that's what we need to win."
The Islanders managed only five shots in the third. Right after Ellis' goal, Nashville's Matt Hendricks was assessed a double minor for high-sticking, giving New York a four-minute power play.
"We had a four-minute power play that didn't generate much, which is not good enough," Tavares said. "We have to find a way to get better in those areas at those times in the game."
Nashville LW Viktor Stalberg made his season debut after missing the first four games because of a shoulder injury. After playing three seasons for the Chicago Blackhawks, Stalberg signed a four-year deal with Nashville in July. ... Capuano coached in his 200th NHL game. ... Tavares has a four-game point streak.
Copyright by STATS LLC and The Associated Press
NASHVILLE, TN - OCTOBER 12: (L-R) Assistant coaches Phil Housley and Lane Lambert of the Nashville Predators watch...