Amadio received a pass from Tim Stutzle in the left circle and buried a one-timer at 16:51.
Shane Pinto scored, and Samuel Ersson made 24 saves for the Senators (10-6-1).
Peyton Krebs scored, and Colten Ellis made 28 saves for the Sabres (7-5-3), whose three-game winning streak ended.
Krebs gave Buffalo a 1-0 lead at 14:00 of the second period when Tage Thompson’s shot from above the slot deflected off his leg in front past Ersson blocker side.
Pinto tied it 1-1 at 11:33 of the third period. Ellis stopped Philip Tomasino’s shot, but the rebound popped out in front and Pinto swept a backhand by Ellis’ left skate.