Brady Tkachuk and Max Veronneau scored, and Craig Anderson made 21 saves for the Senators (28-45-6), who have already been eliminated from Stanley Cup Playoff contention.
"Tonight, we had a few too many turnovers in the game," Senators coach Marc Crawford said. "I think, the giveaways in the game, we had 17. And that's too many for us, especially against a good team. Good teams don't turn the puck over. They don't turn the puck over in opportune times."
Gourde tapped in a backdoor pass from Kucherov into an open net to give Tampa Bay a 1-0 lead at 12:04 of the first period.
"[Kucherov and Point] are so good," Gourde said. "They're so talented, they see the ice so well, they skate, they work hard. I mean, there's nothing much more you can say about them. They're amazing players."
Tkachuk scored with a wrist shot from the top of the right circle that beat Vasilevskiy five-hole to tie it 1-1 at 18:48.
Mikhail Sergachev's wrist shot from the point got through traffic to make it 2-1 at 7:48 of the second period, and Point finished a backhand pass from Gourde at the edge of the crease to make it 3-1 at 13:43.
Veronneau cut it to 3-2 at 4:34 of the third period with a snap shot that went over Vasilevskiy's shoulder from a sharp angle on the power play.
Gourde scored 48 seconds later on a breakaway to make it 4-2, and Steven Stamkos took a cross-slot pass from Mathieu Joseph and scored with a wrist shot to extend the lead to 5-2 at 16:55.
"They make you pay," Senators defenseman Dylan DeMelo said. "Over there, they don't need a lot of looks. Obviously, a very skilled team that plays hard, and that's why they're top of the League."
