It was Pittsburgh's fifth win in its past six games - all without Crosby - and second in three games with both Crosby and Malkin out due to injury.
Long known for their offense, the Penguins have allowed only nine goals in this six-game hot stretch as they head into the All-Star break, having not allowed more than two in any one of those games.
Pittsburgh insists it isn't approaching these tight, low-scoring games any differently than it had even when its offense was stocked with all-world talent.
"I don't think we've really changed much, to be honest," defenseman Brooks Orpik said. "Some guys are maybe getting more ice time and playing different roles like power play and whatnot, but we're playing the exact same way.
"We're not playing any more defensive, but I think guys are just maybe buckled down a little more and their focus is a little better."
Fourth-liner Craig Adams ended the scoreless drought with his third goal of the season at 8:35 of the third period off a rebound of an Arron Asham shot for the Penguins, who have won 10 consecutive home games against New York.
Fleury's 18th career shutout was the second this season in which Pittsburgh scored only once. The Penguins have played nine straight games without Crosby, who finally just lost his grip on the NHL scoring lead. They are 5-3-1 since he began feeling the effects of a concussion.
The Penguins have won two of the most recent three without Malkin (knee, sinus infection), who it was announced Tuesday, like Crosby, would miss the All-Star game this weekend in Raleigh, N.C.
"We're a better team with Sid and Geno, that's no secret," Adams said. "But it shouldn't change the way we play."
The rebound bounced off the stick of Dustin Jeffrey to Adams, who was open in the slot.
Adams' shot beat Poulin low to the stick side on the left side of the net.
"It just kind was bouncing everywhere and I was screened and it hit someone," Poulin said. "Sometimes it's hard to stop those."
The Islanders fell to 1-3 in a stretch of five games in seven days that concludes at home against Carolina on Wednesday.
Pittsburgh was held to two goals or fewer for the fifth time in nine games without Crosby. But Fleury improved to 22-5-2 in his past 29 starts. He has allowed two goals or fewer in 21 of them - but his only other shutout in that span came Nov. 24 at Buffalo.
"It seems like the last couple of games I couldn't get a shutout, so it was a treat to finally get one," Fleury said.
Among Fleury's best saves were when he stretched to stop Frans Nielsen with his pad with 2 minutes left in the first. Then, with about 5 minutes left in the second, Fleury stopped Blake Comeau's redirection. The All-Star also withstood a late flurry by New York in the final minute and an extra attacker on.
"He's just had a long period of time where's he's been really solid and the backbone of our team," Penguins coach Dan Bylsma said.
Poulin made 30 saves, keeping the Islanders - who have lost four of five - in the game.
Poulin could have been in the minors by now had Evgeni Nabokov reported to the team after he was claimed off waivers from the Detroit Red Wings. On Tuesday, the Islanders suspended the 35-year-old goaltender, who had signed a one-year contract with Detroit on Thursday.
"I thought Kevin controlled his rebounds really well and it looked like he was seeing the puck pretty good tonight," Islanders coach Jack Capuano said.
Notes: Pittsburgh is 25-8-6 against the Atlantic Division-rival Islanders since the 2004-05 lockout, 16-2-2 home. ... The Islanders are the team that broke Crosby's 25-game point streak in the team's most recent meeting Dec. 29. Crosby played in the Winter Classic against Washington on New Year's Day and against Tampa Bay on Jan. 5, but sustained hits to the head in both games that led to his concussion. ... New York has allowed the first goal in 10 of 11 games. ... The Islanders have not won in Pittsburgh since Dec. 21, 2007.