Late in third period, it was announced that Crosby, at 19 years, 5 months, became the youngest player elected by fans to the All-Star Game.
"It's an honor. Growing up watching it, and who would have dreamed of playing in it?" Crosby said. "It's something I will enjoy."
Vincent Lecavalier and Andreas Karlsson also scored for Tampa Bay, which has an 11-game winning streak against Pittsburgh. Five of the victories have come at home, where Tampa Bay has outscored the Penguins 22-4.
St. Louis has four goals and 11 points during a personal eight-game point streak. The Lightning have won two straight, both against the Penguins.
"We need to get on a run," St. Louis said. "Winning two in a row is a start."
Crosby put the Penguins up 1-0 just 24 seconds in. He took the puck away from Tampa Bay defenseman Dan Boyle near the blue line and scored with one knee on the ice while being hooked from behind in the low slot.
Colby Armstrong also scored for the Penguins, who have lost four of their last seven.
"We are only getting scoring from one line right now," Pittsburgh coach Michel Therrien said. "The other three lines score once every three games."
St. Louis gave Tampa Bay a 2-1 lead on his 27th goal during a power play at 6:46 of the second. His shot from along the goal line deflected off Pittsburgh goalie Marc-Andre Fleury.
Tampa Bay's Johan Holmqvist made a diving save on Mark Recchi's back-hander with 17:04 left in the third. Karlsson extended the Lightning lead to 3-1 19 seconds later with his first goal in 19 games. St. Louis set up the goal by stealing the puck from Pittsburgh defenseman Sergei Gonchar.
"The third goal was an important one," Lightning coach John Tortorella said. "We tried to get a two-goal lead. I guess the formula is to try and get everyone to contribute offensively and defensively, and I think that happened tonight."
Armstrong got Pittsburgh within 3-2 with 2:41 to play.
Holmqvist made 29 saves.
"He was a big part of the team, definitely," Lecavalier said. "He played really well."
Lecavalier tied it at 1 at 6:11 of the first. He has 20 goals in 31 career games against Pittsburgh.
Fleury stopped 21 shots.
Crosby has four goals and 10 points in his five-game points streak. ... The Lightning have won seven of their last 11. ... Lightning captain Tim Taylor sat out with a lower-body injury. ... Pittsburgh center Evgeni Malkin had a five-game point streak end. He had two goals and seven points over the stretch.