All of the scoring took place in the opening 20 minutes with the Capitals remaining unbeaten in their four games this season. The Senators have just one win in five tries.
Backstrom scored on the power play 8:47 into the contest and Johansson put a wraparound shot past Alex Auld less with 7:59 to go in the first.
Peter Regin delivered Ottawa's goal with only 26 seconds remaining in the opening period.
Vokun, who has been in goal for three of Washington's wins, made 33 saves. Auld allowed the two goals on 26 shots.