Malone deflected Sami Salo's blue-line slap shot at 3:39 of the third that pulled the Lightning even at 4. Tampa Bay took a 5-4 lead when the left wing scored from the low left-circle with 7:02 to play.
Tom Pyatt extended the lead to 6-4 with a late empty-net goal. Tampa Bay (3-1) has outscored its opponents 11-1 in the third this season.
Matt Carle, Steven Stamkos and Victor Hedman also scored for the Lightning, who started a five-game homestand.
Ottawa, which had a season-opening three-game winning streak end, got goals from Erik Condra, Jason Spezza, Erik Karlsson and Kyle Turris. Daniel Alfredsson, with two assists, has 45 assists and 68 points in 57 games against Tampa Bay.
The teams combined for five goals over the final 5 1/2 minutes of the second.
After Spezza scored from the left circle on a 4-on-3 power at 14:30 of the second, Karlsson gave the Senators a 3-1 advantage 15 seconds later during a 4-on-4.
Spezza has 19 goals and 42 points over 31 games against the Lightning.
Stamkos followed with his goal 15 seconds after Karlsson scored with both teams still short-handed one skater, but Ottawa regained a two-goal lead when Turris got his fourth goal this season at 17:30.
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Hedman then cut the deficit to 4-3 with 1:50 left in the second.
Ottawa had not allowed a goal during the second and third in its previous three games this year.
Carle stopped a personal 57-game goal drought to put the Lightning up 1-0 during a power play 69 seconds into the game.
Condra scored his first goal in 16 games on a breakaway at 4:11 of the second.
Lightning rookie Cory Conacher had two assists and has a point in all four games (five assists, seven points) this season.
Notes: Tampa Bay C Vincent Lecavalier was honored before the game for playing in his 1,000th NHL game at the New York Islanders last Monday. Lecavalier, who received several gifts including an engraved silver stick, is the 280th player in league history to reach the milestone. ... It was a battle of tall goalies: Ottawa's Ben Bishop is 6-foot-7, while Tampa Bay's Anders Lindback is 6-6.
Press; By MARK DIDTLER]
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