Sanderson, who returned to the Ottawa lineup on April 4 after missing 13 games with an upper-body injury, set a new career high for goals with his 12th and 13th of the season.
Tim Stutzle had a goal and two assists, and Jordan Spence and Fabian Zetterlund also scored for the Senators (41-27-10), who have won three of their past four games. Drake Batherson had two assists, and Linus Ullmark made 28 saves.
Nick Paul and Corey Perry each had a goal and an assist for the Lightning (48-24-6), who have lost three of five. Jonas Johansson made 25 saves
Spence gave the Senators a 1-0 lead at 15:46, burying a wrist shot over Johansson's glove from the edge of the right face-off circle that bounced quickly off the back bar.
Paul tied it 1-1 at 18:23. Perry's attempted pass from the left circle deflected off the skate of Tkachuk to Paul in front, where he lifted a backhander to the glove side.
Zetterlund put Ottawa back up 2-1 at 2:45 of the third period when his wrist shot from above the left circle deflected off the right hand of Lightning defenseman Erik Cernak and dipped through the pads of Johansson. Cameron Crotty had the secondary assist for his first NHL point in his fourth game.
Sanderson made it 3-1 at 4:39 after skating down the right side and around Tampa Bay defenseman J.J. Moser to the front of the net. Moser hit Sanderson's stick, which caused the puck to come loose and trickle under Johansson's left pad from in tight.
Perry cut the deficit to 3-2 at 10:35, redirecting a pass from Ryan McDonagh over Ullmark's blocker from the left of the crease.
Stutzle pounced on a loose puck and scored a power-play goal from in front at 12:51 to push the lead to 4-2. The Lightning challenged for goaltender interference, but the goal was upheld after video review.
On the ensuing power play, Sanderson extended it to 5-2 just 13 seconds later at 13:04. He took a pass from Tkachuk and finished a forehand-backhand deke from in tight for his second goal of the game.
Shane Pinto scored a short-handed, empty-net goal at 16:41 to secure the 6-2 final.
