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Steven Stamkos had an empty-net goal, and Simon Gagne added two assists for the Lightning, who have won two in a row after a four-game losing skid.
"Little by little we're building back up," Moore said. "Again, it's no secret, it's all about work and effort. Earning victories and deserving wins."
Tampa Bay would have clinched a playoff berth if Carolina, which beat Washington 3-2 in shootout, had lost in regulation.
"It's for another day," Stamkos said. "We're comfortable with our game right now. Seems like we've got our confidence back. There's a lot of positives."
The Lightning play Pittsburgh, a potential first-round playoff opponent, on Thursday night.
"We know that we've got a good chance of playing each other, so we'll definitely learn from each other," Tampa Bay captain Vincent Lecavalier said. "It's pretty close to playoff time. I'm sure it's going to be a pretty intense game."
Ottawa, last in the Eastern Conference, got goals from Jason Spezza and Milan Michalek. The Senators dropped to 6-4-1 over their last 11.
"They got a couple of lucky goals," Spezza said. "They played well, but I don't think it's a 5-2 game. We deserved better than that."
St. Louis put the Lightning up 1-0 on an in-close goal at 3:15 of the second. Just 14 seconds later, Tampa Bay goalie Dwayne Roloson made a glove save on Ryan Shannon's shot from the left circle.
Moore made it 2-0 with 12:35 left in the second. Marc-Andre Bergeron's shot went off the end boards and rebounded into the crease, where Moore poked the puck into the net while goalie Curtis McElhinney was trying to control it with his glove.
"I still think I had it covered to begin with," McElhinney said. "Sometimes that's the way it goes."
St. Louis extended Tampa Bay's advantage to 3-0 on his 29th goal of the season 5:48 into the third. St. Louis scored off a pass through the slot from Gagne.
After Spezza scored with 9:57 left, Tampa Bay responded with Moore's second of the game, 1:24 later.
"They just made good on their opportunities," Ottawa coach Cory Clouston said. "Unfortunately we didn't have any puck luck."
Michalek scored a short-handed goal later in the third. Tampa Bay has given up 16 short-handed goals.
Stamkos, who has just four goals in 22 games, scored his 44th this season with 33.9 seconds left. Stamkos also ended a five-game point drought earlier with an assist on St. Louis' third-period goal.
Lightning LW Ryan Malone is expected to return Thursday after missing 21 games with a mid-body injury. ... McElhinney, claimed by Ottawa off waivers from the Lightning on Feb. 28, had beaten Tampa Bay twice earlier this month. He never played with the Lightning after being obtained in a trade with Anaheim on Feb. 24. ... Bergeron stopped his 11-game point drought. ... Lecavalier had an assist to extend his point streak to five games (five assists, seven points).
Copyright by STATS LLC and The Associated Press
Arena: Amalie Arena Location: Tampa, Florida
Referees: Rob Martell, Mike Leggo Linesmen: Tim Nowak, Dan Schachte
Attendance: 16,626 (86.6% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Martin St. Louis (28)
Assists: Vincent Lecavalier, Simon Gagne
Dominic Moore (16)
Assists: Marc-Andre Bergeron, Dana Tyrell
Martin St. Louis (29)
Assists: Simon Gagne, Steven Stamkos
Jason Spezza (17)
Assists: Colin Greening, David Hale
Dominic Moore (17)
Assists: Dana Tyrell, Brett Clark
Milan Michalek (17)
(Shorthanded) Assists: Filip Kuba, Jason Spezza
Steven Stamkos (44)
(Empty Net) Assists: Adam Hall, Dominic Moore