Tyler Kennedy and Matt Cooke also scored for Pittsburgh, which has won five consecutive and eight of nine.
Malkin returned to the lineup after missing the previous five games due to a left knee injury and a sinus infection, but he was knocked out of the game during the first shift of the second period with a lower-body injury after a collision with Sabres defenseman Tyler Myers.
In the first 7 minutes of playing without Malkin, the Penguins - 9-1 without him this season - scored three times.
Paul Gaustad and Mike Grier scored for Buffalo, playing its first game in 10 days.
Malkin appeared to be skating hard throughout the first period - generating a game-high three shots to that point - but he was a minus-2 as Pittsburgh trailed 2-0.
Twenty-one seconds into the second, Malkin gingerly left the ice after Myers fell awkwardly onto his left leg. Jeffrey scored 3:29 later, using his speed to skate down the right wing and throw a shot toward Buffalo goalie Ryan Miller that would deflect off of Sabres forward Tim Connolly's skate.
Kennedy tied it 2:34 later with his second goal in as many games, beating Miller with a wrist shot from the right-wing circle for his ninth of the season.
Forty seconds later, Cooke gave Pittsburgh its first lead with his 10th. Jordan Staal set up the play with a steal and pass to Cooke in the left slot. Cooke corralled the puck on his forehand and slid it through Andrej Sekera as he turned it over to his backhand. He then flipped the puck up into the far portion of the net.
Since the Sabres last played, the franchise was sold and rookie Tyler Ennis represented the team in Raleigh, N.C., for All-star weekend.
Buffalo didn't come out rusty, scoring on the first shift of the game and adding another 7:03 in.
Gaustad's sixth of the season and second in three games came after Alex Goligoski turned the puck over to Rob Niedermayer, who fed Gaustad in the slot.
Grier was credited with the goal that made it 2-0, his first since Nov. 11 and third of the season, when he came from behind the net and threw it into the crease, the puck deflecting off of the skate of Pittsburgh defenseman Deryk Engelland and past Penguins goalie Marc-Andre Fleury.
Fleury made 27 saves to win his seventh consecutive start, allowing only 12 goals in that time and improving to 25-11-2.
Notes: Two nights before the Steelers play in the Super Bowl, the Penguins encouraged fans to bring Terrible Towels to the game and aired a video tribute wishing good luck to the Steelers on the scoreboard. ... Jeffrey, a rookie, has five goals in 10 games this season, three in his past five. ... Pittsburgh has won five in a row at home and five straight against Buffalo. ... The Sabres entered on a 9-3-1 run, having won two consecutive and four of five.