Drew O'Connor put Pittsburgh ahead 1-0 at 2:40 of the first period, putting in the rebound of Rust’s shot with a backhand in the crease.
Raymond tied it 1-1 at 3:39 with a backhand in front.
Kris Letang gave Pittsburgh a 2-1 lead at 15:09 with a wrist shot from the slot.
Raymond tied it 2-2 at 19:46, taking a pass from DeBrincat on a 2-on-1 rush and going forehand to backhand around Nedeljkovic’s right pad.
Crosby put the Penguins back in front 3-2 at 7:58 of the second period, tapping in a pass from Rust at the left post.
Crosby has 1,591 points (591 goals, 1,000 assists) in 1,269 games, passing Phil Esposito (1,590 points; 717 goals, 873 assists) for 10th in NHL history.
“Just think about that for a second,” Pittsburgh coach Mike Sullivan said. “That puts him in real elite company. The milestones that he’s achieving now, I think they’re self-explanatory. It puts him in just elite company of the greatest players of all-time.”
Rust made it 4-2 at 12:44 with a snap shot from the high slot.
Jeff Petry cut it to 4-3 at 19:24 on a slap shot from the top of the right circle.
Jeff Carter extended the lead to 5-3 at 3:32 of the third, scoring short-handed with a wrist shot from the right circle.
"It was extremely frustrating,” Larkin said. “We're on the power play, we're trying to get back in the game, (and) we give up a shorty this time of year. ... When you get a power play in the third, we have to get something going and we didn't get it going.”
NOTES: Crosby needed the seventh-fewest games to reach 1,000 NHL assists (1,269 games). Only Wayne Gretzky (645), Mario Lemieux (856), Paul Coffey (1,105), Adam Oates (1,174), Ron Francis (1,235) and Marcel Dionne (1,259) reached the mark faster. Crosby is also the seventh player to have 1,000 assists with one team. ... Larkin passed 500 points in the NHL. He has 502 points (211 goals, 291 assists) in 649 games.