Brayden Point and Mikhail Sergachev scored for the Lightning (42-25-6), who have lost three straight. Brian Elliott made 28 saves.
Tampa Bay is in third place in the Atlantic Division, five points behind the second-place Toronto Maple Leafs, who won 6-2 at the Florida Panthers on Thursday.
"It's unfortunate, we're having a little tough stretch here, but it's all self-inflicted," Lightning coach Jon Cooper said. "Not sure when they are going to learn. There's a little bit of us feeling sorry for ourselves."
DeBrincat gave the Senators a 1-0 lead at 8:53 in the first period when he scored off a wrist shot to finish a 3-on-1 rush.
He extended the lead to 2-0 at 11:37 when he fought off defenseman Zach Bogosian to get a shot past Elliott.
"I thought we played pretty good from start to finish and played well in our zone too," DeBrincat said. "I felt like our line did pretty well. It's been tough to get them by the goalies lately.
Debrincat hadn't scored since March 9, ending a seven-game goal drought. The Senators are 17-1-1 when he scores this season.
"I guess I've got to score more," DeBrincat said. "Obviously, this year hasn't been as good for me, offense-wise. Still trying to do what I can to help the team win. We've been doing a good job battling against the top teams each night, trying to pull out some wins."
Point made it 2-1 at 10:28 of the second period with a one-timer from the left circle off a pass from Nikita Kucherov.
Derick Brassard gave Ottawa a 3-1 lead with a power-play goal at 18:04, a one-timer that rang off the far post and in.
Sergachev cut it to 3-2 with a power-play goal at 4:10 of the third period, a one-timer from center point.
Erik Brannstrom answered for the Senators at 5:45 with a goal from the high slot to make it 4-2, his first goal in 19 games (Feb. 11).
"It's fun to play some offensive hockey and contribute out there," Brannstrom said. "It was great for us. We had a lot of good efforts from a lot of the guys tonight. We have to keep going with the push here."
Tkachuk made it 5-2 with a power-play goal at 13:11 and extended the lead to 6-2 with an empty-net goal at 13:35.