O'Reilly scored on a wrist shot 4:26 into the final stanza for a 4-1 cushion, after which Ottawa's Nick Foligno and Ryan Shannon tallied to give the Senators a chance at what would have been their third win in a row.
Craig Anderson then closed the door for Colorado, which won its second in a row and its sixth out of eight. Anderson made 27 saves for his 19th victory.
Matt Duchene, Kyle Quincey and Chris Durno also scored for Colorado before O'Reilly grabbed a rebound off a missed shot by Brandon Yip and delivered his fifth goal of the campaign.
The loss went to Pascal Leclaire, who made 16 saves.
Colorado improved to 8-2-1 against teams from the Eastern Conference. It was the fourth straight road win for the Avalanche.