Backstrom scored both goals in the third period and assisted on Mike Knuble's goal at 17:46 of the first.
Boyd Gordon and Alexander Ovechkin also scored goals, while Jose Theodore gave up two goals on 28 shots for the Capitals, who have won two straight and have a 14-point advantage over Atlanta atop the Southeast Division. To date, they have scored an NHL-leading 154 goals.
Ottawa got one goal apiece from Chris Phillips and Jonathan Cheechoo.
Pascal Leclaire was beaten five times on 38 shots for the Senators, who have lost two of three.
On the power play, teams went 0-for-3.