Eller redirected Artem Zub's shot from the right point under the glove of Ukko-Pekka Luukkonen to make it 2-1 at 5:55 of the third.
Ridly Greig (17:42) and Shane Pinto (18:42) added empty-net goals for the 4-1 final.
Dylan Cozens also scored for the Senators (39-26-10), who had lost three in a row (0-2-1). Linus Ullmark made 21 saves.
The Senators moved into the second wild card from the Eastern Conference with the win. They are tied in points with the Detroit Red Wings and Columbus Blue Jackets but own the tiebreaker over both. Columbus held the spot entering the night but lost 5-1 at the Carolina Hurricanes.
Mattias Samuelsson scored the lone goal for the Sabres (46-22-8), who had won two straight and were looking to clinch a playoff spot for the first time since 2011. Luukkonen made 20 saves.
After a scoreless first period during which Buffalo outshot Ottawa 6-4, the Sabres struck first in the second.
Samuelsson took a pass from Bowen Byram at the left point, skated to the top of the circle, and scored through a screen to give Buffalo a 1-0 lead at 8:49.
Cozens tied the game 1-1 at 15:18 of the second. Greig knocked down Rasmus Dahlin's clearing attempt at the left point and passed over to Brady Tkachuk, who then sent a feed down low to Cozens, who had gotten behind Dahlin and redirected the puck with one hand on his stick past Luukkonen.
Senators defenseman Tyler Kleven left the game with an upper-body injury in the first period after blocking a shot up high from Bowen Byram. Kleven joins a long list of injured defensemen for the Senators, which includes Jake Sanderson (upper body), Nick Jensen (lower body), Dennis Gilbert (upper body), Thomas Chabot (upper body), and Carter Yakemchuk (upper body).
