Nashville has won two of three. The Islanders were beaten for the third time in four games — including twice in two days.
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 19-year-old defenceman, who was the No. 4 four pick in this year's NHL draft, 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.
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.
NOTES: 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. ... New York's Jack Capuano coached in his 200th NHL game. ... Tavares has a four-game point streak.