"There's no way you can beat that team if the goaltender is not at his best," Tampa Bay coach Guy Boucher said. "They've got everything, basically. We've got to play almost perfect defensively."
Pittsburgh got a third-period goal from Tyler Kennedy.
It was the first game between the teams since Roloson helped Tampa Bay beat Pittsburgh in an Eastern Conference quarterfinal series last season.
"Last year is last year," Roloson said. "We're focusing on this year."
There was some chippy play, but no fights took place.
Roloson stopped an in-close shot by Steve Sullivan in the first. He also made several strong saves, including a lunging pad stop on Sullivan's back-hander, during a late second-period power play.
"I don't think we had any quality chances," Pittsburgh defenseman Kris Letang said. "I think we took some shots, but I don't think he had a really difficult life back in his net."
Lecavalier put the Lightning up 1-0 from just outside the crease on Tampa Bay's first shot of game 8:38 into the first. He picked up a loose puck after a defensive-zone turnover by Jordan Staal and made several moves before beating goalie Marc-Andre Fleury.
Fleury finished with 14 saves. He was 7-0-1 in his previous eight games.
Connolly made it 2-0 when he re-directed Dominic Moore's shot while positioned in the low slot during a power play at 4:08 of the second.
Connolly had lost his stick shortly before the goal and went to the bench area, where high-scoring Steven Stamkos handed the rookie right wing his stick.
"There's a lot of magic in those sticks, for sure," Connolly said.
Pittsburgh had allowed just three goals in 53 previous short-handed situations this season before Connolly's goal.
Downie extended the lead to 3-0 on Tampa Bay's second power-play goal of the game early in the third.
Pittsburgh has given up power-play goals in only three games this season. Toronto had two man-advantage goals in a 4-3 win on Oct. 29, and Washington had one Oct. 13 en route to a 3-2 overtime victory.
"Clearly the special teams battle ... two power-play goals for them and us not cashing in on our opportunities," Penguins coach Dan Bylsma said. "A lot of them came late and we were pressing at that point in time, but they won the battle 2-0 and that's pretty much the difference in the game."
Pittsburgh went 0 for 7 on the power play, while the Lightning converted two of their six opportunities.
After Lecavalier scored his second goal of the game into an empty net at 15:49 of the third, Kennedy ruined Roloson's bid for his 30th career shutout a minute later.
"They've got great players," Downie said. "It's always nice to beat these guys."
Pittsburgh C Sidney Crosby, who hasn't played since Jan. 5 because of a concussion, continues to work out with the team. ... Lightning LW Ryan Malone missed his fourth straight game due to an undisclosed upper body injury. He did take part in a morning practice. ... Downie ended his 16-game goal drought. ... Penguins LW James Neal had his seven-game point streak snapped. He had four goals and 11 points during the stretch.