Rutger McGroarty gave Pittsburgh a 2-1 lead 19 seconds into the second period with a wrist shot from the high slot for his first point in six games this season.
Kevin Hayes then made it 3-1 at 9:42, tapping in a pass from Noel Acciari, and Rust scored on a one-timer set up by Crosby to extend the lead to 4-1 with a power-play goal at 19:53.
Crosby reached 1,721 NHL points (644 goals, 1,077 assists), putting him two behind Mario Lemieux (1,723 points; 690 goals, 1,033 assists) for the most in Penguins history.
“You know they’re going to push,” said Crosby, the Penguins captain. “We’ve just got to be better with their goalie pulled. We’ve got to close out games. There’s lots of ways to do that. We’ve got to be better there.”
Pittsburgh has blown a third-period lead in three of its four straight losses. The Penguins led 2-1 before the Dallas Stars tied it at 18:11 of the third in a 3-2 shootout loss on Sunday, and began a five-game homestand with a 4-3 shootout loss to the Anaheim Ducks on Tuesday, when Karlsson accidentally gloved a puck into his own net for a short-handed, tying goal with 0.1 seconds left in regulation.
“Obviously, we have to be better closing out games,” Penguins coach Dan Muse said. “Like, that doesn’t need to be stated. I think it’s something different every time. I don’t think it’s always the exact same thing. ... The common thread is we get away from what works.”
NOTES: The Sharks recorded the fifth-latest four-goal comeback win in NHL history, behind the Los Angeles Kings (rally started at 12:46 of the third period on Nov. 10, 2007), Buffalo Sabres (11:25 of the third on March 10, 1976), Dallas Stars (10:01 of the third on Oct. 21, 1993) and New York Islanders (8:21 of the third on March 14, 1987). ... San Jose forwards Philipp Kurashev and Will Smith each left the game with an injury. Kurashev (upper body) exited at 8:24 of the second after sliding into the end boards, and Smith left at 3:30 of the third after taking a hit from Pittsburgh defenseman Parker Wotherspoon. There was no update on either. ... Sharks defenseman Dmitry Orlov had two shots on goal and played 22:41 in his 900th NHL game. ... Penguins goalie Stuart Skinner and defenseman Brett Kulak were granted nonroster status due to immigration issues after being acquired from the Edmonton Oilers on Friday with a second-round pick in the 2029 NHL Draft for goalie Tristan Jarry and forward Samuel Poulin. ... Pittsburgh forward Rickard Rakell had three shots on goal and played 22:13 in his return from missing 20 games following surgery on his left hand Oct. 26.