TAMPA, Fla. -- Tampa Bay coach Guy Boucher could sense from the start that the Lightning were poised to stop a seven-game losing streak.
"We had emotion," Boucher said. "We have a lack of confidence from losing some games and I told the players I didn't care about the score. I wanted fight. When the puck dropped, we're going to fight."
Moore stopped an 11-game goal drought and put Tampa Bay up 4-3 when he beat Tim Thomas with a shot from the top of the left circle.
"Obviously, when things aren't going your way, confidence is always something that's an issue," Moore said. "The only way you get it back is be positive."
Steven Stamkos added his NHL-leading 31st goal of the season into an empty net during the final minute of play.
Boston had been especially strong this season during the third, outscoring opponents 62-27 in the period entering Tuesday.
"We played a good team and really responded," Stamkos said. "That was the game plan, to come out hard, come out physical. We did that for pretty much the whole 60 minutes, and that's the result that we get."
Nathan Horton had two goals and Daniel Paille added a short-handed goal for the Northeast Division-leading Bruins, who were coming off a 3-2 shootout win at Florida on Monday night. Horton has 24 goals and 44 points in 44 games against Tampa Bay.
"Our compete level isn't there," Boston coach Claude Julien said. "We're no better and no worse than any other team when we don't compete. We become a very ordinary team, and that's what we are right now."
After Malone scored off a turnover 4:58 into the third, Paille got the Bruins even at 3 on a backhand during his short-handed breakaway at 10:53.
Paille has two of Boston's six short-handed goals this season. Tampa Bay has given up seven goals to its opponents while on the power play.
Tampa Bay went up 2-1 when Thomas was unable to cover the puck after a diving attempt and Pyatt chipped home a backhand from just outside the crease with 5:49 left in the second.
Thomas is 2-4 in his past six games.
"If there's one thing that you can put a finger on, then it would be easy to fix," Thomas said. "It's not. It's a whole bunch of little things adding up and combining together."
Horton pulled Boston even at 2 just 2:37 after Pyatt's goal. He had tied it 1-all on an in-close rebound earlier in the second at 4:28 after Mathieu Garon stopped the right wing's initial shot.
David Krejci, who had his 11-game point streak end (five goals, 16 points) Monday night, assisted on Horton's second goal of the game.
Lecavalier put the Lightning ahead 1-0 with a backhand from the slot at 7:11 of the first. The center also hit the post from the right circle during a power play late in the period.
"They came out hungry tonight, and it showed from the first period," Paille said. "The whole game, we were trying to catch up with them in scoring. They fought hard."
Stamkos had his pass during a 3-on-1 go off a Bruins defender, Thomas and the post midway through the second.
This was the first time the teams had played each other in Florida since the Bruins beat Tampa Bay in last season's Eastern Conference finals.
"They didn't look like that against us," said Thomas, when asked if the Lightning resembled a team on a long winless stretch. "We looked like that."
- Tampa Bay RW Martin St. Louis has gone 12 games without a goal, but has 14 assists, including one Tuesday, during that stretch.
- Boston LW Brad Marchand served the final game of a five-game suspension for a hit on Vancouver's Sami Salo on Jan. 7.
- Lecavalier has 20 goals and 48 points in 47 games against Boston.
- Bruins C Rich Peverley missed his second straight game tending to a personal matter.
- Tampa Bay D Marc-Andre Bergeron (back) sat out for the third consecutive game.