Glen Murray scored for Boston, which lost for the second time in six games.
"They made things happen," Bruins coach Claude Julien said. "Our best players weren't our best players tonight. It's pretty simple. When you lose games like that, that's normally what happens."
Lecavalier stole an errant pass by Boston defenseman Zdeno Chara deep in the Bruins zone. After Tim Thomas stopped Lecavalier's first shot, the Lightning center scored on the rebound to put Tampa Bay ahead 1-0 at 5:45 of the first.
Tampa Bay went ahead 2-0 on Lecavalier's power-play goal with 4:07 left in the period.
Lightning goalie Johan Holmqvist made several strong saves during the first period, including a low slot shot by Vladimir Sobotka. He finished with 28 saves.
"It starts with Homer," Tampa Bay defenseman Shane O'Brien said. "Homer was awesome."
Lecavalier was hit in the face in the neutral zone with 18:28 left in the second. He underwent treatment on the bench for the welt below his right eye before returning to the ice a few minutes later.
"He's a tough kid," Darche said.
Murray cut the Bruins' deficit to 2-1 on the power play at 17:47 of the second. The Lightning got the goal back when Darche scored with 58.6 seconds remaining in the period.
St. Louis extended the Lightning's advantage to 4-1 with his first goal in six games, scored at 6:13 of the third. Lecavalier set up the goal for his 300th NHL assist.
Thomas had 24 saves.
The Lightning have had two six-game losing streaks this season. ... Savard had an assist, extending his point streak to nine games. He has 14 assists and 16 points over the stretch. ... Bruins LW Milan Lucic (concussion) missed his fourth straight game. ... Boston D Aaron Ward left with an undisclosed injury. He will be evaluated on Sunday.
Copyright by STATS LLC and The Associated Press
Arena: Amalie Arena Location: Tampa, Florida
Referees: Stephane Auger, Dean Warren Linesmen: Steve Barton, Brian Mach
Attendance: 18,444 (96.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Vincent Lecavalier (17)
Vincent Lecavalier (18)
(Power Play) Assists: Brad Richards, Michel Ouellet
Glen Murray (7)
(Power Play) Assists: Dennis Wideman, Marc Savard
Mathieu Darche (3)
Assists: Filip Kuba, Chris Gratton
Martin St. Louis (9)
Assists: Vincent Lecavalier, Paul Ranger