Malkin scored with 12:50 remaining to make it 3-1, turning a giveaway by Marc Staal into a backhander under the crossbar, and added an empty-netter with 1:40 left. Malkin has 24 goals this season, including seven in four games.
"It's always hard to play against the Rangers," Malkin said. "It's tough because they have a great team and they are the best team now in the NHL.
"We deserved to win because we played better in the third period. We shoot more and we have scoring chances more. It's a great feeling."
Fleury played in his 19th straight game for the Penguins, who have won four in a row following a six-game skid.
"I feel all right," Fleury said. "I don't count them. It's a lot more fun now that we're winning, definitely."
Carl Hagelin scored New York's lone goal, and Lundqvist made 32 saves for the Eastern Conference-leading Rangers, 2-3 since a 10-1 spurt. This was their first game since a win over Nashville on Tuesday prompted team owner James Dolan to suggest the Rangers (29-12-4) were "pretty close" to the Stanley Cup title.
The Penguins, who have been hit hard by injuries to captain Sidney Crosby, forward Jordan Staal, and others, got good news with the return of defenseman Kris Letang. Letang had missed 21 games since sustaining a concussion on Nov. 26 at Montreal.
In other games *
At Newark, N.J., Nathan Horton and Gregory Campbell scored in a 35-second span in a four-goal third period that carried Boston to a 4-1 victory over the New Jersey Devils.
Defenseman Andrew Ference tied it at 3:01 of the period and Horton and Campbell put the Bruins ahead for good as they beat New Jersey for the third time in three games this season.
