Brady Tkachuk and Claude Giroux also scored, and Thomas Chabot and Artem Zub each had two assists for the Senators (25-21-7), who have won two in a row after losing four of five (1-2-2). James Reimer made 16 saves in his fifth start in six games.
Valeri Nichushkin and Parker Kelly scored for the Avalanche (35-7-9), who have lost five of their past seven games (2-3-2). Mackenzie Blackwood made 18 saves.
After a scoreless first period in which Ottawa outshot Colorado 9-4, the Senators struck first in the second.
Nick Cousins gave Ottawa a 1-0 lead at 3:21 after he collected a long stretch pass from Zub at the blue line, skated in and beat Blackwood with a backhand.
Kelly tied it 1-1 at 14:05 when a dump-in by Keaton Middleton was tipped by Brock Nelson and landed on the stick of Kelly, who snapped a shot past the blocker of Reimer. It was his third goal in five games.
Just 17 seconds later, Ridly Greig restored Ottawa’s lead, 2-1 at 14:22. Greig won a race to the puck against Middleton after it caromed off the end boards behind Blackwood and lifted a shot over the goalie’s right shoulder.
Giroux extended it to 3-1 at 2:06 of the third period, finishing into the top left corner on a 2-on-1.
However, Nichushkin cut it to 3-2 at 3:30 following a Giroux giveaway. His clearing attempt found the tape of Jack Drury, who passed to Nichushkin in the slot for a backhand over the glove of Reimer to end a 10-game scoring drought.
Tkachuk scored into an empty net to make it 4-2 at 17:44, and Stutzle added another empty-net goal at 18:53 for the 5-2 final.