Crosby, who began the day as the league's No. 3 scorer with 79 points, has missed three games due to a left groin injury.
Malkin more than compensated for Crosby's absence, earning the primary assist on goals by Jordan Staal and Kris Letang, and striking on the power play in the second period. He has 92 points in 64 games.
"We're playing right now without Sid - an outstanding player - and eventually we will get him back and add to how we're playing," said interim coach Dan Bylsma, 5-1-1 since getting the job on Feb. 15. "We still need to get better and better going down the stretch."
Miroslav Satan also scored for Pittsburgh, 2-0 on its five-game road trip. The Penguins jumped over Buffalo and Carolina into eighth place in the Eastern Conference.
"We have to keep improving if we want to make the playoffs," Fleury said. "We've had such a tough time and a battle to get back into contention."
Malkin said the Penguins must concentrate on immediate goals and not look too far ahead.
"The trophy is not the thing right now, the two points are the thing," Malkin said.
The Stars lost their season-high fifth straight, finishing a 1-5 homestand during which they fell below the postseason cutoff line in the West. Dallas has scored six goals during its slide.
"Teams are smelling blood when they play us and feel we're down and out," Stars center Mike Modano said. "They feel if they play well, we'll lay over and bow out. That ought to be incentive for us to surprise some teams. We're at a crossroads right now. We need to heighten the alert level and the desperation level."
The Stars open a three-game road trip on Tuesday against Pacific Division rivals San Jose, Los Angeles and Anaheim.
"Nobody's feeling sorry for us," Dallas defenseman Stephane Robidas said. "Nobody's going to give us a game. It's a big trip coming up. We're in a tough spot right now. We didn't have any emotion this afternoon."
Loui Eriksson scored a power-play goal for the Stars, breaking Dallas' 0-for-20 drought with the man advantage.
Rookie Tobias Stephan stopped 19 shots for Dallas in his first start since Dec. 13. Marty Turco had made 32 consecutive starts before getting a break on Sunday.
Staal fired the rebound of Malkin's shot past Stephan at 4:08 of the opening period for his 17th goal.
Letang made it 2-0 at 16:21 of the first period, skating in alone from the right side off a pass from Malkin and backhanding a shot by Stephan.
Satan took advantage of a turnover by defenseman Trevor Daley to extend the lead to 3-0 at 8:18 of the second period. Daley mis-hit a pass attempt, and the puck landed on the stick of Satan, who went in by himself and tapped a shot into an open net for his 17th.
Malkin connected from the slot through Stephan's pads at 12:38 of the second period. His 29th goal gave the Penguins a 4-0 edge.
Dallas avoided its sixth shutout of the season when Eriksson registered his 28th at 6:02 of the third.
The Stars were without center Steve Ott, suspended indefinitely by the NHL after he received a penalty for attempting to injure Anaheim's Travis Moen at the end of a game on Saturday.
Ott won't be eligible to play until after a hearing with league officials that will determine a specific length of the ban.
Notes: This was the only meeting between the teams this season. Pittsburgh was playing in Dallas for only the second time since 2003. ... Crosby was injured in a game against Washington last weekend. He skated before Sunday's game and said he's feeling better, but he's still not ready for game action. ... Penguins RW Petr Sykora remained in the lineup despite an upper-body injury that kept him out of practice on Saturday.