Jake Guentzel and Brandon Hagel also scored, and Nikita Kucherov had two assists for the Lightning (29-20-4), who have won three of four, including a 4-3 victory against Ottawa here on Tuesday. Andrei Vasilevskiy made 27 saves.
Hagel (Canada), Point (Canada) and Guentzel (United States) will represent their respective countries in the upcoming 4 Nations Face-Off from Feb. 12-20.
"It was a massive two games for us," Tampa Bay coach Jon Cooper said. "We had this five-game homestand, we dropped the first one to Chicago, but for us to get seven out of the next eight [points] was pivotal. Especially against a division rival that we're neck-and-neck with. And they were hot coming in."
Michael Amadio scored for the Senators (29-22-4), who have lost consecutive games after winning five straight. Anton Forsberg made 26 saves.
"The score was 5-1, but we played a pretty good game," Ottawa coach Travis Green said. "I hate saying that when you lose 5-1, but it's a 2-1 game with five minutes left. We played a lot better tonight than we did in the first game."
Guentzel gave Tampa Bay a 1-0 lead with a power-play goal at 9:23 of the first period when he poked in a loose puck off a rebound of a shot from Point.
"Obviously a great effort, this was a huge two games for us," Guentzel said. "This is our identity; we've got to not give up much because that's a high-scoring team over there. I think it's easy to get up for these games...playoff mentality against a team we're fighting against."