Tampa Bay would have clinched a playoff berth since 2007 if Carolina, which beat Washington 3-2 in shootout, had lost in regulation.
"It's for another day," Stamkos said of clinching the playoff berth. "We're comfortable with our game right now. Seems like we've got our confidence back. There's a lot of positives."
The Lightning host 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," captain Vincent Lecavalier said. "It's pretty close to playoff time. I'm sure it's going to be a pretty intense game."
"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."
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 shorthanded goal later in the third. Tampa Bay has given up a League-high 16 shorthanded goals.
Stamkos, who has just 4 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.
Material from wire services and team media was used in this report
|Martin St. Louis (28) ASST: Vincent Lecavalier (27), Simon Gagne (17)|
1 - 0 TBL
|Dominic Moore (16) ASST: Marc-Andre Bergeron (5), Dana Tyrell (8)|
2 - 0 TBL
|Martin St. Louis (29) ASST: Simon Gagne (18), Steven Stamkos (44)|
3 - 0 TBL
|Jason Spezza (17) ASST: Colin Greening (6), David Hale (3)|
3 - 1 TBL
|Dominic Moore (17) ASST: Dana Tyrell (9), Brett Clark (22)|
4 - 1 TBL
|SHG - Milan Michalek (17) ASST: Filip Kuba (12), Jason Spezza (31)|
4 - 2 TBL
|EN - Steven Stamkos (44) ASST: Adam Hall (10), Dominic Moore (13)|
5 - 2 TBL
|Nick Foligno Slashing against Steven Stamkos|
|Milan Michalek Tripping against Nate Thompson|
|Mattias Ohlund Roughing against Colin Greening|
|Victor Hedman Delay of game|
|Chris Neil Elbowing against Steve Downie|
|Chris Neil Roughing against Steve Downie|
|Chris Neil Fighting (maj) against Steve Downie|
|Chris Neil Misconduct (10 min) against Steve Downie|
|Steve Downie Fighting (maj) against Chris Neil|