Lack, who started Vancouver's most recent game Friday in New Jersey, was sharp from the minute he came in. He made five saves in the first two minutes and had 19 in the third period.
"Eddie was unbelievable today," Canucks coach Willie Desjardins said. "He made some unbelievable saves."
Miller sustained a lower-body after he was run into by teammate Jannik Hansen, who crashed into the net and made contact with Miller's right leg. Miller, who got the win, made 10 saves for Vancouver (33-22-3) before being replaced by Lack. The Canucks continue their five-game road trip at the Boston Bruins on Tuesday.
"We want to make sure we evaluate it right but he probably won't be in [Tuesday]," Desjardins said.
It was the Canucks' first shutout since Feb. 7, a 5-0 win against the Pittsburgh Penguins. Lack credited his teammates' defensive effort. Vancouver had 16 blocked shots.
"A lot of guys stepped up," Lack said. "It was just a great team effort. A lot of the guys blocked shots in front of me."
Vancouver scored three times in the second period, including twice on the power play.
Zach Kassian scored his third goal in two games at 28 seconds on a man-advantage with a slap shot from inside the blue line to the right of Islanders goalie Jaroslav Halak. The shot hit the left post, then Halak's back before trickling past the line.
Forward Radim Vrbata scored his 22nd on a power play at 9:53. He took a shot from just inside the left point on a pretty passing play from Daniel Sedin and Henrik Sedin, who each picked up assists on the play.
It was the second power-play goal the Islanders allowed in the game after having not allowed one in their previous six games, going a perfect 14-for-14 on the penalty kill. New York was 1-for-3 on the penalty kill and 0-for-5 in 9:51 of power-play time.
"At the end of the day, we have to do a better job on special teams," Islanders coach Jack Capuano said. "As you move forward, and in the playoffs, that is what it's going to come down to."
Bo Horvat scored to increase the Canucks' lead to 3-0 at 13:55. Defenseman Dan Hamhuis dumped the puck in around the boards behind the Islanders net, which was played by Hansen, who passed to Ronalds Kenins. Kenins fed Horvat and his wrist shot eluded Halak from inside the right point.
The Islanders pulled Halak with almost four minutes remaining to try and generate some offense while on a power play, but Yannick Weber added an empty-net goal at 19:49.
Halak made 20 saves for the Islanders (39-20-2), who were shut out for the second time this season, and first since a 5-0 loss against the Colorado Avalanche on Oct. 30.
"You have to put in your opportunities when you get them and we didn't, and they did more often than not," Islanders captain John Tavares said. "We weren't able to get that first one and put the pressure on."
Vrbata had a goal and an assist and Henrik Sedin had two assists for the Canucks.
"We don't want to put [Nielsen] in a position where he can hurt himself further so once we evaluate it, we'll have a better idea," Capuano said.
Vancouver defenseman Luca Sbisa was hit in the mouth with the puck while sitting on the bench and went to the dressing room midway through the third period, but returned to the bench toward the end of the game.
The Canucks improved to 2-1-0 on their five-game road trip.
"We went to New York and we beat the Rangers (last Thursday)," Henrik Sedin said. "They are a tough team, a tough loss the night after (in New Jersey). Then we played one of the best teams in the League here. And with all the injuries we have to come in here and earn the win, that's impressive."
Lack was aware that he probably will start Tuesday at Boston.
"I hope I can step up," Lack said. "I don't know if it's even going to be a game [that Miller is out]. … Just take it day-by-day here and see what's going on."
Follow David Satriano on Twitter: @davidsatriano