San Jose outshot Ottawa 21-8 in the second.
"Anytime [the other team] scores a goal, or at the end of a period, I think it's important for the next shift that you play the way we want to play," Senators forward Claude Giroux said. "We play in our structure, and we have a good game plan. We just have to execute out there."
Couture scored an empty-net goal with 59 seconds left in the third period for the 5-1 final.
Kahkonen, who allowed nine goals over his previous two starts, made 17 saves in the third.
"I think his confidence early on, even about a week and a half ago, was not where it needed to be," Quinn said. "And he's built his confidence up. He's worked hard. He's done a really good job."
NOTES:Karlsson had an assist and is tied for the third in the NHL with 29 points. Edmonton Oilers center Connor McDavid leads with 35 (16 goals, 19 assists). … Couture has scored in four straight games and has 10 goals this season.