Fleury stopped 27 shots to tie Tom Barrasso's franchise record for career shutouts, and Malkin scored his 33rd goal of the season as the Penguins beat the Rangers 2-0 on Tuesday night.
"We wanted to make a statement with every shift, every period we play against them," Bylsma said.
Pittsburgh topped the Rangers at home for the first time since 2009 behind Fleury, who made a series of flashy glove saves while earning his 22nd career shutout -- tying the mark Barrasso set between 1988-2000. Barrasso reached the milestone in his 438th game, but Fleury needed only 418 to get there.
"For me to be able to reach him for the shutout means a lot to me," Fleury said. "I've been fortunate to play with good teams."
The Penguins looked like one two days after getting crushed 6-2 in Buffalo. Needing to bounce back, Pittsburgh played with a sense of urgency, dominating the puck at times against a team that is among the best defensive units in the league.
"I think that was our first complete 60-minute game in a long time," said Pittsburgh forward Steve Sullivan, who scored a power-play goal in the second to give the Penguins a 2-0 lead. "We got something from everybody."
The Rangers didn't, and lost for the second time in three games. They pulled out an overtime win against Columbus on Sunday after allowing the tying goal late in regulation.
New York coach John Tortorella refused to point fingers even though his club has scored only five goals during the stretch amid speculation the Rangers could acquire Columbus forward Rick Nash before Monday's trade deadline.
"We ended up with some good chances tonight, we just couldn't finish," Tortorella said. "Their goalie played well."
So did New York's Henrik Lundqvist, who stopped 29 shots but was no match when Malkin raced in alone on a breakaway early in the second period. The Russian, the league's leading scorer, faked a forehand and then held onto the puck while dragging it across the goal mouth. He finished with a backhand after Lundqvist committed.
"If he's shooting the first second I'll be fine, but he kept waiting, waiting, waiting and I ran out of gas on that push," Lundqvist said.
The Rangers have been one of the hottest teams over the last three months behind Lundqvist and a patient, selfless defense that began the night fourth in the NHL in blocked shots.
New York added 14 more on Tuesday repeatedly hitting the ice to take away opportunities -- particularly in the first period. Pittsburgh spent more than two minutes in the Rangers' zone during one sequence while both teams were at even strength, sapping New York's energy so much that Tortorella was forced to use his timeout early.
"The first period we had a tough time keeping the puck," Tortorella said. "Some of it was the puck was bouncing around both teams. We just didn't keep it, and they won a number of them in the offensive zone. That's where they surged on us."
The timeout helped New York settle down, but a sloppy play by defenseman Michael Del Zotto a minute into the second put Pittsburgh on the board. Nearing the end of his shift, Del Zotto flipped the puck into the center of Pittsburgh's zone. Two quick passes found Malkin streaking down the left side, and Lundqvist was scrambling.
"It's always a challenge to face this team especially because of him. He's one of the best in this league if not the best," Lundqvist said. "As a goalie you go in with the mindset you have to be sharp or it's going to be a long night."
The goal ended a mini-slump for Malkin, who went three games without scoring. It was his longest drought since going seven games between goals from Dec. 17 and Jan. 7.
Sullivan made it 2-0 with his 11th of the season on the power play, just past the midway point of the period. He fired a shot from the point that Lundqvist never saw because of a screen by Matt Cooke. Malkin slid the puck over to Sullivan on the play to earn his 40th assist of the season and 300th of his career.
Pittsburgh has been treading water over the last three weeks, good one game, bad the next. The Penguins romped past Philadelphia on Saturday, getting production from outside the top line. The team celebrated by signing forward James Neal to a six-year contract extension on Sunday shortly before getting smashed by the Sabres.
If they want to play deep into spring they know they will need to play with the intensity that marked their first win over New York on home ice since Nov. 28, 2009.
"(The Rangers) are the best in the East right now by a margin," Bylsma said. "We feel like we're going to play this team two more times (in the regular season) and in the playoffs, too, if we want to go somewhere."
The Penguins have three days off before continuing a homestand on Saturday against Tampa Bay. ... The Rangers will visit the New York Islanders on Friday, trying to avoid their first losing streak since Dec. 13 and 15. ... The Penguins scratched defenseman Brooks Orpik because of an undisclosed upper body injury that Bylsma described as minor.