The Senators took a 2-1 lead at 14:22 of the second period when Ridly Greig scored from the slot off the rush.
Claude Giroux doubled Ottawa's lead with a right-circle shot off the rush at 2:04 of the third period.
The Avalanche cut its deficit in half at 3:30 of the third period when Nichushkin scored his 12th goal of the season via a backhand shot from the doorstep after receiving a pass from Jack Drury, who started the play with an offensive-zone interception.