Washington has won three in a row and is 7-0-2 in its past nine games. Holtby has been in net for all of them.
Backstrom broke a 1-1 tie with 35 seconds left in the second period during a power play. He has 11 goals this season, including six in his last five games. Beagle made it 1-0 at 13:59.
Mike Green assisted on both Capitals goals.
Erik Condra scored his third goal of the season to tie it 1-1 in the second period, and Craig Anderson stopped 21 shots for Ottawa. The Senators are 3-3-1 since Dave Cameron replaced Paul MacLean as head coach.
Beagle opened the scoring after he snared a long pass from Evgeny Kuznetsov. Despite having Ottawa's Jared Cowen draped over him, Beagle managed to fire a shot that deflected in off Anderson's left pad for his fifth of the season.
The Senators tied it less than two minutes later when Condra stripped the puck from Green at the Capitals blue line, skated in alone and scored.
Alex Ovechkin then drew a holding penalty on Eric Gryba at 18:08, and Backstrom's high wrist shot from the right circle beat Anderson.
Washington was outshot 14-6 in the first period despite three power plays, including a 5-on-3 advantage for 1:06.
Ottawa's power play failed in the period, as well, largely because of to Holtby.
With the Capitals down a man, he grabbed Clarke MacArthur's one-timer against the post at 4:32. The save stood up to a video review that confirmed he didn't catch the puck over the goal line.
Minutes later, with the Senators on another power play, Holtby made a pad save against Kyle Turris off a point-blank rebound try.
NOTES: Washington recalled C Andre Burakovsky and LW Aaron Volpatti from Hershey of the AHL. Volpatti (upper body) will return to the team's injured, non-roster list and long-term injury list. ... The Capitals will begin a three-game trip on Tuesday at the New York Rangers, and return home to play the Chicago Blackhawks in the Winter Classic on New Year's Day. ... The Senators are off until Saturday when they host the Detroit Red Wings.