Lecavalier had a power-play goal at 4:53 in overtime, Stamkos scored his NHL-leading 40th goal and the Lightning beat the St. Louis Blues 4-3 on Sunday.
Tampa Bay, which leads the Southeast Division by three points over Washington, was coming off a 5-2 loss Friday night to the Capitals.
"Personally, for myself, I thought that was one of my worst games last game in a big game, so I knew I had to come out and try to prove to myself that I wanted to help this team win," Stamkos said. "It wasn't just me, the whole team stepped up."
St. Louis defenseman Eric Brewer was called for a holding penalty 3:40 into the extra session, and Lecavalier converted a rebound backhander off a shot by Marc-Andre Bergeron for his ninth goal of the season, giving Tampa Bay the victory.
"Relentless, that's how we played," Lecavalier said.
Lecavalier has two goals in his last 17 games.
"The difference is a 4-on-3 goal with 6 seconds left in overtime," Backes said. "There's no such thing as a moral victory, but to see ourselves play straight up with a prety good team is a step in the right direction."
Stamkos, who turns 21 on Monday, 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 the Blues, 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.
"We got a point," St. Louis coach Davis Payne said. "I think there's a lot of good things to take out of this hockey game. We've got to make sure we take them down the road."
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. ... Bergeron, recalled Saturday from Norfolk of the AHL, made his Lightning debut and had two assists in his 400th NHL game. "When you have a chance to play for a team like this at this time of the year, I'm going to do everything that I can to make the best out of it and help these guys to win," Bergeron said. ... 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.