NASHVILLE, Tenn. (AP) Point after precious point, Nashville keeps climbing up the standings.
Ryan Ellis and Austin Watson also scored for Nashville, which has recorded at least one point in the standings in 16 of their last 17 games. With the victory, Nashville closed to within three points of the idle Chicago Blackhawks for third place in the Central Division.
The Predators played their first home game after a two-week long road trip.
''I really liked the way we played,'' Nashville coach Peter Laviolette said. ''Coming off the road trip, you never know what you're going to get, but I thought we were pretty sharp from start to finish.''
Rookie Ryan Pulock and Brock Nelson had the goals for the Islanders, who have lost of four of their last five.
Neal scored the game's first goal at 9:15 of the opening period. Calle Jarnkrok carried the puck off of the right wall and from the circle, he fed Neal skating through the slot, where he beat Thomas Greiss with a wrist shot on the stick side. Neal was coming off of his first hat trick of the season in Nashville's win Monday at Edmonton.
Pulock tied it at 1 at 6:02 of the second with a wrist shot from the right point for his first career NHL goal. John Tavares assisted on the goal, giving the Islander captain his 30th of the season - the sixth time he has reached the mark.
''For sure, obviously not the outcome we wanted, but for myself, it's good to get the first one out of the way,'' Pulock said. ''It's one I'll remember forever for sure, so that's exciting.''
Nashville regained the lead at 8:13 of the second on a power-play goal by Ellis. From the top of the right circle, Ellis fired a slap shot by Greiss on the stick side.
''I've been working on that and our power play has been a little cold as of late,'' Ellis said. ''We got back down to basics and shot pucks and it seemed to work.''
Johansen followed 1:41 later when he lifted a wrist shot under the crossbar from just outside the crease on the right side.
Early in the third, Nelson squeezed a wrist shot from the right circle through Rinne to cut the Nashville lead to one.
Following Nelson's goal, New York only managed one more shot on goal the rest of the game.
''It's been the same theme for us, it's the common denominator that we try to make the sexy play and we don't want to get pucks to the net,'' Islanders coach Jack Capuano said. ''Give them a lot of credit. Every time they got an opportunity, the puck was on net. That's how you create zone time.''
Watson added an empty-net goal with 56.4 seconds remaining to seal the victory for Nashville.
Greiss had 28 saves, while Rinne finished with 20.
''I thought that all night long we played a strong game,'' Rinne said. ''They battled back, but it was a solid home game.''
NOTES: The Islanders selected Pulock with the 15th overall pick in the 2013 draft. ... The Islanders are 9-3-1 against the Central Division this season. ... Nashville is 24-1-3 when leading after two periods. ... Predators D Anthony Bitetto has a point in three of his last four games.