Dumont scored from the slot 1:52 into the third to break a scoreless tie, and Patrick scored his third of the season at 2:06.
Ottawa defenseman Wade Redden scored for the third consecutive game, pulling the Senators within one with a power-play goal at 4:10. Ottawa's last eight goals have come with the man advantage, including a team-record five Thursday night against Columbus.
Buffalo ended a three-game winless streak. The Sabres have won only twice in their last seven games (2-2-2-1).
The Senators, who fell to 0-6 in one-goal games, lost their second in a row. Ottawa is 2-5-2 since winning five of its first seven games.
Biron came up with a big stop on former teammate Vaclav Varada's chance early in the second, and made a pad save moments later on Daniel Alfredsson's shot from the edge of the crease.
Sabre center Daniel Briere set up Dumont's goal early in the third. Briere moved from behind the net and passed from the right side of the net to Dumont, who beat Senator backup Martin Prusek through the legs for his fourth of the season.