The Predators have won three straight and are 6-0-2 in their last eight games. New York has lost six in a row and 20 of 21 (1-17-3).
Lindback made it back-to-back shutouts two nights after stopping 22 shots in a win over the Florida Panthers on Saturday. The rookie from Sweden has won three straight and is 4-0-1 since taking over for No. 1 Predators goalie Pekka Rinne, who is out with a knee injury.
"I feel like the whole team is really stable, and we go out every night and do what we have to and work really hard," Lindback said. "I feel like I am pretty good in my positioning and tracking the first pucks. I'm trying not to leave too many bad rebounds out there."
Kostitsyn gave Nashville a 1-0 lead at 11:15 of the opening period.
With the Predators on a power play, Cody Franson had the puck at the right point. He moved to the high slot and fired a shot that was deflected in front by Kostitsyn. It got past Islanders goalie Dwayne Roloson on the glove side to extend Kostitsyn's point streak to a career-best six games.
"The first goal was really huge," Nashville coach Barry Trotz said. "If they score on the first couple of shifts there, it might be a totally different attitude. They are a young team and they have some dynamic guys like John Tavares. We don't know the players as well from the East, we don't play them a lot."
New York is 0-15-2 in games it trailed 1-0.
"I think we have slides where out of 60 minutes we will play 50 minutes or 45," Islanders defenseman James Wisniewski said. "It's not all in the whole 15 minutes or 10 minutes that we don't play well, it's three minutes in the second or four minutes in the first or something where people take advantage."
Hornqvist doubled the Nashville lead at 5:22 of the second period.
From the high slot, defenseman Shane O'Brien sent a wrist shot on goal. Roloson made the stop, but Hornqvist gathered the rebound and put a shot into the open net for his seventh goal.
Just over two minutes after Hornqvist's goal, Smithson made it 3-0.
"We had a tough night back there. I'm not going to lie to you," Islanders coach Jack Capuano said of the team's defensive effort. "We had a lot of giveaways, we didn't move the puck fast enough, and we didn't let the puck do the work. That is why in the second period, we spent most of the time in our end."
Hornqvist and Spaling added third-period goals. Spaling netted his first NHL goal in his 50th career game.
"It's great," Spaling said. "It's pretty exciting to get that. I'm just glad to get one."
Nashville RW Martin Erat had an assist to extend his point streak to three games. ... The Predators haven't allowed a power-play goal in 12 of 13 games. ... Islanders rookie RW Rhett Rakhshani made his NHL debut after being called up from AHL Bridgeport earlier Monday. ... New York D Mark Eaton, who played five seasons with the Predators, missed his first game of the season because of a groin injury.