Fleischmann netted his 12th and 13th goals of the season in the first two periods where the Capitals (21-7-6) took a 5-0 advantage to cruise to the road win.
"When you're playing a high-potency offensive team, you have to give them the low percentage, and that is the other side of the ice," Avalanche captain Adam Foote told reporters of facing the NHL's highest scoring team.
"They are the type of team. If you give them those opportunities, with their talent, they are going to put it in the net."
The Southeast Division leaders got early scores from Mike Knuble, David Steckel and Matt Bradley.
Colorado's T.J. Galiardi put his team on the board in the third where Nicklas Backstrom capped the scoring on a power play.
The Avalanche (19-11-6) still remain two points clear in the Northwest despite having their two-game win streak snapped.
Washington goaltender Jose Theodore made 27 saves against his former team while Capitals defenseman Mike Green left the game in the second after being checked into the glass and sustaining a cut near his eye.
The NHL's top scoring defenseman, Green was hit by Colorado's David Koci much to the dismay of Washington coach Bruce Boudreau.
"So I hope they throw the book at him. If this was a (competitive) game he gets on the ice, gets into a fight and sits at the end of the bench. So what good is he?"
(Writing by Jahmal Corner in Los Angeles; Editing by Alastair Himmer)