Tyler Ennis and Mike Reilly had a goal and an assist for Ottawa (18-23-9), which went 3-for-4 on the power play. Craig Anderson made 28 saves.
The Senators, who lost 4-3 in a shootout at home against the New Jersey Devils on Monday, are 2-1-4 in their past seven games.
"We've been in a lot of games. We kind of strung out some overtime losses there and gotten some points," Anderson said. "We haven't been rewarded for our efforts, but we've just got to keep striving to get better and get rewarded for the good hard work, and that's what it was tonight."
WATCH: [All Senators vs. Sabres highlights]
Linus Ullmark made 30 saves for Buffalo (22-21-7) but fell awkwardly in his crease and left the game at 10:28 of the third period because of a lower-body injury. Carter Hutton made four saves in relief.
"It's always painful to watch that kind of situation," Sabres coach Ralph Krueger said of Ullmark, who will be evaluated Wednesday. "We'll see and we'll work through it with him now."
The Sabres, who played their first game since Jan. 18, trail the Carolina Hurricanes by 10 points for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
"We can't play like that at home, a team coming off a back-to-back. We just had a break," said Buffalo captain Jack Eichel, who scored his 29th goal of the season, an NHL career high. "It's not good enough. I mean, if you want to make the playoffs, that's not a playoff-caliber effort by us. You know that, I know that, everyone in the room knows that."