Malone deflected Sami Salo's blue-line slap shot at 3:39 of the third that pulled the Lightning even at 4. Tampa Bay, which has outscored opponents 11-1 in the third this season, took a 5-4 lead when the left winger scored from the low left-circle with 7:02 to play.
"We go back to the game plan of just playing simple hockey," Malone said.
Tom Pyatt extended the lead to 6-4 with a late empty-net goal.
"They're character guys, and they like a great challenge," Lightning coach Guy Boucher said.
Matt Carle, Steven Stamkos and Victor Hedman also scored for the Lightning, who started a five-game homestand. Stamkos added two assists, giving him six assists and eight points this year.
"We weren't very good or consistent from start to finish, although we did have the lead twice at two goals," Senators coach Paul MacLean said. "The other team flat outplayed us."
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 in 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.
Hedman then cut the deficit to 4-3 with 1:50 left in the second.
"We let them back in it, and that's the frustrating part," Senators right Chris Neil said.
Unlike the strong third periods, the Lightning have been outscored 10-3 during the second.
"We don't play 200 feet of hockey," Boucher said of his team's middle-period play. "Our attitude is going to change."
Ottawa had not allowed a goal during the second and third in its previous three games this year.
"I didn't particularly like anybody today," MacLean said of his team. "I don't think there's any individuals that were better or worse than others."
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.
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. ... Salo tied a team record by going plus-5 in the game.
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TAMPA, FL - JANUARY 25: Nate Thompson #44 of the Tampa Bay Lightning warms up with teammates before the game...