Crosby got an empty-netter with 0.1 seconds to play. His goal came following a tense net-mouth scramble in which the Devils nearly tied the game.
Crosby surpassed Evgeni Malkin and Mario Lemieux for the most 20-plus goal seasons in franchise history. He's the 36th player in NHL history to have 13 or more 20-plus goal seasons.
''It's hard to score 20 goals in this league,'' Penguins coach Mike Sullivan said. ''I don't think it's ever routine. I think guys that reach that milestone consistently are really good players.''
Jeff Carter, who was acquired by Pittsburgh in an April 12 trade with the Los Angeles Kings, scored his 10th of the season and second in three games. Casey DeSmith stopped 34 shots and Jared McCann scored a power-play goal for the Penguins, who have 13 wins and points in 15 of their last 18 games overall.
Pittsburgh completed a three-game series sweep of New Jersey. The Penguins, who have points in their last nine home games, have nine wins in their last 12 games against the Devils.
New Jersey dropped its ninth straight game and 13th in 14 games overall. Miles Wood scored his 15th goal for the Devils, and Jack Hughes got his 11th.
Mackenzie Blackwood made 36 saves for the Devils after missing the previous two games with an upper-body injury. He is winless in his last nine starts since March 30.
''We need to step up here and get a win, because quite frankly, I'm sick and tired of losing hockey games,'' Wood said.
Carter opened the scoring at 9:41 of the first period. The puck rolled off Jason Zucker's stick and went to Carter, who beat Blackwood to the blocker side from the right faceoff dot.
McCann scored his team-leading seventh power-play goal 3:09 after Carter's goal. McCann nearly shouldered the right post as he dove and converted a point-shot rebound over Blackwood's pad. It was McCann's 13th goal overall.
Rust gave Pittsburgh a three-goal lead 7:30 into the second. Jake Guentzel initially deflected Cody Ceci's point shot, which later hit Rust's shin pad and went into the net.
Hughes made it 3-1 at 8:45 of the second. The puck slipped off Yegor Sharangovich's stick and went to Hughes, who beat an out-of-position DeSmith.
Wood pulled the Devils within a goal 10:58 into the third period. DeSmith committed to the initial shot from Ryan Murray, but he slid a pass to Wood, who scored on a one-timer. Damon Severson's assist tied Ken Daneyko for seventh in Devils history for points by a defenseman.
''I think everybody is tired of losing, but the effort we put in, the detail we put in, kept the game close and gave ourselves an opportunity,'' Devils coach Lindy Ruff said.
CROSBY MAKES HISTORY
Crosby's late goal also locked in his 16th season averaging at least a point a game.
Crosby, who has 55 points in 47 games, joins Wayne Gretzky as the only players in NHL history to have a point-per-game season in each of their first 16 years in the league. Gordie Howe averaged a point-per-game in 17 seasons total, one more than Crosby.
''Anytime you're mentioned with Gordie Howe and Wayne Gretzky, that's pretty neat,'' Crosby said. ''It's a compliment to be in that company.''
Sullivan called Crosby a generational talent.
''All these milestones he's achieving is more evidence of the legacy he's built and the stamp that he's put on the game,'' Sullivan said. ''Some of these milestones he's reaching now is in such elite company, he is, in my mind, building a real compelling argument for being one of the greatest players of all time.''
Malkin skated before Saturday's game.
Malkin wore a no-contact jersey a day earlier when he joined the team at practice for the first time since suffering a lower-body injury on March 16.
Brandon Tanev and Frederick Gaudreau, who have missed 10 and six games, respectively, also skated before Saturday's game.
Devils center Janne Kuokkanen missed Saturday's game after injuring his hand blocking a shot on Thursday. Defenseman Jonas Siegenthaler also did not play because he was added to the COVID-19 protocol list.
HITTING THE MARK
Rust has scored 20 goals in consecutive seasons. Rust, who netted a career-high 27 goals in 2019-20, is two away from 100 for his career.
Rust has points in 12 of the last 13 games - nine goals and 17 points - against the Devils, including 10 straight. Guentzel also has points in nine consecutive games against the Devils. He has 10 goals and 25 points in 21 career games against New Jersey.
''I can't think of another guy that has developed his game as much as (Rust),'' Sullivan said. ''He's always been a solid player, but he's developed his offensive game so well over the time that I've been with him.''
Devils: Visit Philadelphia on Sunday for the first of four games against the Flyers.
Penguins: Continue a five-game homestand Sunday against Boston.
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