Crosby had three goals and an assist and Matt Niskanen scored a tiebreaking power-play goal with 18.6 seconds left, lifting the Penguins to a 5-4 victory over the Tampa Bay Lightning on Saturday night.
"It was evident today for us," Penguins coach Dan Bylsma said of Crosby's leadership.
Niskanen scored from the top of the left circle, with Crosby getting an assist.
"We kind of have a little bit of a plan on what we want to do on the power play, and for the most part we just kind of read and take what's there," said Niskanen, who scored for the first time in 22 games.
Crosby tied it at 3 with a knee-high re-direction of Rob Scuderi's shot 25 seconds into the third, and then put Pittsburgh in front when he scored from the right circle with 9:34 remaining. It was his eighth career hat trick.
"Pucks are going to be around there," Crosby said about playing near the net. "It's not an easy place to go, and you're going to have to force yourself to go there as much as you can. Luckily there was some pucks around there, and I was able to get some good quality chances from there."
Crosby has a point in all five games this season. It's his longest point streak to start a season since a six-game stretch in October 2005.
"I think that was an even hockey game," Tampa Bay coach Jon Cooper said. "They got that last break at the end and capitalized on it."
Brooks Orpik scored for the Penguins (4-1), who lost 6-3 Friday night at Florida.
Orpik stopped a 110-game goal drought dating to Nov. 21, 2011, when he tied it at 2 just 1:50 after Stamkos' goal. The defenseman has 12 career goals in 636 NHL games.
Tampa Bay took a 3-2 lead on Purcell's knee-high deflection during a power play with 4:18 to go in the second.
Stamkos, coming off a hat trick in Thursday's 7-2 victory over Florida, gave Tampa Bay a 2-1 lead from the right circle at 5:11 of the second.
Crosby tied it at 1 with an in-close power-play goal 2:14 into the second.
"They, obviously, have some world-class players over there," Tampa Bay left wing Ryan Malone said.
Pittsburgh D Kris Letang and RW Matt D'Agostini, both sidelined by lower-body injuries, practiced. ... Tampa Bay G Ben Bishop (3-0) is hopeful of returning for Tuesday's game against Los Angeles. Bishop said he felt pretty good after taking shots in practice Saturday, two days after his right leg got jammed during the third period Thursday night. ... Malone and Pittsburgh's Craig Adams fought 4 seconds into the game. ... Malone also received a 10-minute misconduct after a scrum early in the second.