Jordan Spence, Fabian Zetterlund, Tim Stützle and Shane Pinto also scored for Ottawa (41-27-10). Brady Tkachuk had four assists and goaltender Linus Ullmark made 27 saves for the win.
Nick Paul and Corey Perry scored for the Lightning (48-24-6). Jonas Johansson made 25 saves.
Tied 1-1 to start the third, the Senators scored twice in less than two minutes to take a two-goal lead.
Zetterlund came across centre, took a pass at the blueline and let a shot go that went off Erik Cernak to beat Johansson five-hole.
Just over one minute later, Sanderson drove to the net and held off J.J Moser to slide the puck in short side for his 12th of the season and a career-high in points.
“It’s awesome,” Sanderson said post-game, after fans chanted for the playoffs in the dying seconds of the game. “It fires all the guys up here in the room and we want that too. We’re playing good hockey right now so we’ve just got to keep doing it for the rest of the four games.”
Perry pulled the Lightning within one midway through the third when he was left all alone and raised a shot over a sprawled Ullmark.
The Senators added a pair of power-play goals to secure the victory.
Stützle jumped on a loose puck at 12:51 to make it 4-2. Tampa lost a goaltender interference challenge and Sanderson scored his second of the game on the ensuing power play.
Pinto scored into an empty net.
“I’ve said it many times in here, they’re a very coachable group,” head coach Travis Green told reporters post-game. “We talk a lot about confidence, like wanting to be in these moments. Our goal isn’t just to make the playoffs — we want to win a Stanley Cup. You’re going to have to play with the spotlight on you. You’re going to have to play in pressure moments and really enjoy those moments. Like, look forward to those moments, want them and embrace them.
“Our team buys in. They’re a fun group to coach.”
Ottawa opened the scoring at 15:46 of the second period when Tkachuk and Spence played give and go on an odd-man rush. Spence finished it with a wrist shot high glove side.
The Lightning tied it less than three minutes later when Perry’s pass went off Tkachuk’s skate to Paul in the slot. Paul quickly backhanded the puck past Ullmark.
Ottawa had a brief scare in the second period when Sanderson took a shot off his left foot and left the game, but he was able to return.
Thomas Chabot skated with the Senators in a non-contact jersey for the first time since his right arm injury sustained March 23.
Senators: Ottawa’s net front presence had a definite impact.
Lightning: The Lightning struggled to generate shots from the inside early in the game.
With an assist on Ottawa’s opening goal, Stützle recorded his second-career 80-point season.
Senators: Host the Florida Panthers on Thursday.
Lightning: Visit the Montreal Canadiens on Thursday.