Bryan Rust deflected a shot from Crosby on a power play, pushing it to 5-1 at 13:31.
"They're a proud group," Penguins coach Mike Sullivan said. "They have an appetite to win. I think, to a man, the core group of players that has been here, they're just hungry to win. They're hungry to win. There's no other way to say it."
Brayden Point cut it to 5-2 at 14:03 before Rickard Rakell scored an empty-net goal with 4:05 remaining for the 6-2 final.
"Started turning the puck over way too much," Point said. "A team like that, that speed coming at you and all that skill, it's tough to defend when you're just giving them rushes."
NOTES:Crosby has 1,415 (519 goals, 896 assists) in 1,110 NHL games, passing Doug Gilmour (1,414 points in 1,474 games) for sole possession of 19th place all-time. He has the most points among active players, ahead of Washington Capitals forward Alex Ovechkin (1,411 points; 780 goals, 631 assists in 1,277 games). The Penguins captain has 423 multipoint games in his NHL career, 101 more than games without a point (322). ... Stamkos' three-game goal streak is the second longest to start a season in Lightning history. Kucherov scored in the first seven games of 2017-18. The Lightning captain moved into sole possession of second place on their all-time assists list (492), behind Martin St. Louis (588). … Penguins defenseman Jan Rutta had two shots on goal and one hit in 15:09 of ice time in his first game against his former team since signing a three-year contract July 13. The defenseman won the Stanley Cup with Tampa Bay in 2020 and 2021.