"We outworked them," the Islanders' Matt Martin said. "They played (Wednesday) night and we were a little fresher than them and we had some young legs in the lineup.
"We tracked hard."
The loss, combined with Tampa Bay's 4-2 win over Philadelphia, hurt the Canadiens' chances of starting the playoffs on home ice. Montreal is second in the Atlantic Division with 98 points and one game left to play, while the Lightning have 97 points with two games remaining.
The Canadiens will need to win their final regular-season game Saturday night at home against the New York Rangers and hope the Lightning lose either Friday night against Columbus or Sunday against Washington.
"You want home ice, you want to go into the playoffs feeling good about your game, and we've got Saturday night to do that," Montreal captain Brian Gionta said.
The Islanders posted their first regulation win in four games, but improved to 7-2-2 in their last 11 games.
The Canadiens, coming off a 3-2 overtime loss in Chicago on Wednesday, came out flat and never got their energy up as they were outshot 30-19.
"It's no fun losing at this time, but sometimes, you're just not good enough," said Thomas Vanek, who was traded to Montreal by the Islanders last month. "You have to give them credit, and at the same time, we (stunk). The coaches prepared us and, I don't know if it was tired legs or we were mentally not there or both, but overall they kept skating hard and putting pressure on us and we didn't have a push back."
The Canadiens also got the bad news that second-line forward Alex Galchenyuk, who appeared to injure his right knee in Wednesday's 3-2 overtime loss in Chicago, will miss the first round of playoffs with what the team called a lower-body injury.
New York held a 9-2 shots advantage early in the opening period, but couldn't beat Carey Price, even when the Montreal goaltender wandered halfway up the left boards and then misplayed the puck.
But Canadiens defenseman Douglas Murray, who returned from a three-game suspension, was ejected at 10:52 of the second period for a check from behind on Johan Sundstrom. The Islanders rookie turned around just as Murray checked him at the side of the net into the end boards.
Sundstrom was injured and taken to a hospital for tests. Coach Jack Capuano said Sundstrom would likely be kept in the hospital for observation and not travel with the team back to New York.
"It was a tough one," Capuano said. "(Murray) is not that type of player. It's one he'd probably like to have back. Hopefully our guy will be all right."
The Islanders used the ensuing power play to open the scoring as Strome put a shot past Price through a screen by Casey Cizikas from the right circle at 15:07.
With Vanek off for high-sticking, Nelson whipped a shot under the cross bar from close range at 19:40.
Canadiens coach Michel Therrien said only Price's solid goaltending kept the score close.
"It was bad performance for our team," Therrien said. "Every aspect of our game wasn't sharp."
Murray drew his first career suspension for an elbow to the head of Tampa Bay's Michael Kostka on April 1. ... The Canadiens end their regular season Saturday at home against the New York Rangers. Tampa Bay plays at home Friday night against Columbus and Sunday against Washington. ... Price and defensemen Andrei Markov and Alexei Elemin, who were given a game off Wednesday in Chicago, were back in the lineup. Forward Lars Eller missed a second game with the flu. ... After the game, the Canadiens returned defenseman Nathan Beaulieu to Hamilton of the AHL.