Backstrom second-period tally broke a 2-2 tie and put the Capitals on the path to the victory, which clinched the Southeast Division crown over the second-place Jets.
The win also locked up the third Eastern Conference seed for Washington.
Braden Holtby turned aside 24 shots in the triumph.
At 51 points with one game to play, ninth-seeded Winnipeg remained one point behind the New York Rangers and Ottawa. The Rangers have two games left while the Senators have three contests remaining on their schedule.
Toddler uninjured after being knocked over by Obama family dog
Florida bear attack: Black bear mauls woman's face