After a monster Game 3, Taylor Hall assisted on Palmieri's goal but didn't have a shot on goal through two periods.
"Kuch tonight flexed his muscles", Lightning coach Jon Cooper said.
Bad blood from Game three carried over into Game four, where seven penalties were called early, including one in the first 34 seconds. Devils' Kyle Palmieritakes advantage of power play to score. Tampa killed the remaining time on the minor and survived a few breaks by Blake Coleman.
BC-HKN-Lightning-Devils, 1st Ld-Writethru, 850Kucherov leads way as Lightning take 3-1 lead over DevilsAP Photo NJJC101, NJJC108, NJJC106, NJJC111, NJJC109, NJJC104, NJJC103, NJJC118, NJJC116, NJJC113Eds: Lightning 3, Devils 1. Stamkos fed Kucherov entering the zone and he found Miller on the left side for a shot over Schneider's shoulder.
This game might have been the roughest of the series, especially in the first period when the Lightning took a 2-1 lead in a session with a lot of scrums. Schneider was excellent in his second start this series, stopping every shot he faced and keeping his team alive.
Cetric Paquette gets 2 mins. for tripping.
The Lightning again won the shot battle in the third period, but it was much closer at 13-10.More news: Turkey snap elections set for 24 June
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Vasilevskiy was ideal in 5-on-5 play, only allowing one goal to Kyle Palmieri in the Devils brief 5-on-3 power play.
Coach John Hynes chose to make the move with New Jersey trailing 2-0 in the best-of-7 series. It did not work.
Kucherov, 24, led the Lightning with 39 goals and 61 assists during the regular season, reaching 100 points for the first time in his career.
The Devils will head back down south with their season on the line.
You couldn't keep your eyes off Nikita Kucherov Wednesday night at the Prudential Center. Butcher now has three points in the series and Hall has five. The difference in the game was the fact that Andrei Vasilevskiy was the best penalty killer for the Lightning in Game 4.
"It was a fun game to be a part of, but it's a little less stressful when you have a one-goal lead", Miller said. Eleven seconds later, New Jersey had its second 5-on-3 goal in two games.
He was still being evaluated on Thursday, and the Devils did not know if he would travel with the team or play in Game 5 on Saturday at Amalie Arena in Tampa, Florida. The Lightning will have a chance to win the series on home ice and move on to the Eastern Conference Semi-Finals.