After assisting on Erik Karlsson's goal 1:04 into the game, Spezza made it 2-0 with a power-play goal at 16:32 of the second period. It was the Senators' first power play goal in seven attempts against Tampa Bay this season. The goal came on Ottawa's first shot on net in more than 12 minutes and ended a surge during which the Lightning had outshot the Senators 9-0.
Spezza's second goal, his 24th of the season, came at 12:37 of the third. He completed the hat trick with 62 seconds remaining when he hit the empty net after Tampa Bay pulled Mathieu Garon.
With his four-point game, Spezza now has 10 points in his last four games.
Anderson has beaten the Lightning in all three games that Tampa Bay and Ottawa have played this season. His 28 saves Tuesday gave him 94 stops on 97 Lightning shots for the season series and a scoreless streak against Tampa Bay that now extends to 71:52. Anderson improved to 6-1-2 lifetime against Tampa Bay.
"We all played a really good game defensively," Anderson said. "You know, when you play solid defensively, you get chances offensively and we showed that tonight."
The shutout was only the second time this season that Tampa Bay was held scoreless and the first time since Nov. 12 in St. Louis. The Lightning hadn't been blanked on home ice since April 2, 2010.
Except for the surge in the second period, the Lightning were unable to generate much extended time in Ottawa's zone, and when they did get a quality scoring chance, Anderson was ready. His best save of the game came in the third period when he denied NHL goal-scoring leader Steven Stamkos from point-blank range.
"We just couldn't score again," Lightning coach Guy Boucher said. "We're playing Ken Dryden when we play Ottawa. Three games in a row we get wide open nets and wide open opportunities, and either he (Anderson) makes a save or we miss the net."
Tampa Bay missed the net with 14 shots and had an additional nine attempts blocked.
The win gave Ottawa (29-22-8) points in its last three games and 66 points overall, good for second place in the East. The Sens continue their three-game road swing against Florida on Wednesday night. Tampa Bay remained at 54 points; the Lightning (24-26-6) started the night eight points behind eighth-place Toronto.
Garon, who has never beaten Ottawa in his career, made 23 saves -- one on Kyle Turris' penalty shot at 11:36 of the final period.
The loss made the Lightning's climb back into a playoff spot that much more difficult, as they continue a crucial four-game homestand against San Jose on Thursday night.
"We worked hard; we missed a lot of opportunities," captain Vincent Lecavalier said. "They got one goal but we definitely got chances to get back in the game; their goalie played pretty solid."
Ottawa coach Paul MacLean agreed.
"I think we played a pretty consistent game from start to finish," MacLean said. "There were some momentum shifts in the game, but Craig Anderson played real well for us."
In addition to opening the scoring, Karlsson also picked up an assist on Spezza's first goal and Bobby Butler earned two assists for the Senators.
But the night belonged to Spezza, who now has goals in his last five visits to Tampa Bay.
"It's a challenge to play against Stamkos, Lecavalier and St. Louis," Spezza said. "You have to be on your game. Some rinks you have a pretty good feel and it always feels like we have some pretty decent success in this rink."
1 - 0 OTT
2 - 0 OTT
3 - 0 OTT
4 - 0 OTT
Interference - Goalkeeper