Crosby scored a power-play goal on a tip-in from the slot at 13:21 of the third period to give the Penguins a 3-2 lead.
Bryan Rust had a goal and an assist, Matt Grzelcyk had two assists and Tristan Jarry made 28 saves for the Penguins (33-35-12), who are 9-4-2 in their past 15 games.
Jake Allen made 17 saves for the Devils (41-31-7), who lost their second straight and are 4-3-0 in their past seven games.
New Jersey is third in the Metropolitan Division and will play the Carolina Hurricanes in the Eastern Conference First Round.
Erik Haula gave the Devils a 1-0 lead just 15 seconds into the first period when he took a pass from Dawson Mercer at the Penguins blue line and skated down the slot before scoring on a snap shot inside the left post.
Ondrej Palat pushed it to 2-0 on a deflection past Jarry after a shot from the high slot by Cody Glass at 6:17 of the first.
Malkin scored for the Penguins to make it 2-1 at 16:10 of the first after poking a puck at the right post that slid onto the outstretched left skate of Allen. Devils defenseman Luke Hughes attempted to clear the puck and inadvertently backhanded it over the goal line.
Valtteri Puustinen made it 2-2 with a power-play goal off a rebound at 1:05 of the second period. Malkin took a shot from the top of right face-off circle that was stopped before it bounced into the net off Puustinen’s left skate.
Rust scored an empty-net goal at 18:24 of the third for the 4-2 final.