St. Louis defenseman Eric Brewer was called for a holding penalty 3:40 into the extra session, and Lecavalier converted a rebound backhander for his ninth goal of the season, giving Tampa Bay the victory.
Stamkos had three assists, and Dominic Moore and Steve Downie also scored for the Lightning, who have won seven of eight. Stamkos also leads the NHL with 72 points.
Patrik Berglund, David Backes and Nikita Nikitin had the St. Louis goals. The Blues have lost 11 of 14.
Stamkos joins Lecavalier (2006-07, 2007-08) as the only Tampa Bay players with consecutive seasons with 40 or more goals. The center has four goals and seven points in three games against the Blues.
Stamkos made it 1-0 with 1:17 to go in the first, lifting a rebound over Ty Conklin after the Blues goalie stopped a shot by Brett Clark. Martin St. Louis, who has 13 assists and 17 points in 15 games against St. Louis, helped set up the goal with a couple of stickhandling moves just above the right circle before passing the puck to Clark.
After Berglund tied it from the low slot 30 seconds into the second, Moore put the Lightning ahead 2-1 at 2:33.
St. Louis tied it again when Backes scored during a 5-on-3 power play at 11:05 of the second. Nikitin (13:09) and Downie (13:39) traded goals 30 seconds apart later in the period.
NOTES: St. Louis G Jaroslav Halak sat out for the second straight game because of an upper-body injury. ... Tampa Bay LW Ryan Malone missed his fifth consecutive game due to a mid-body injury. ... D Marc-Andre Bergeron, recalled Saturday from Norfolk of the AHL, made his Lightning debut and had an assist in his 400th NHL game. ... Nikitin's goal was his first in the NHL, coming in his 17th game. ... Tampa Bay D Mike Lundin is out with an abdomen injury.