The Sabres hit a pair of posts - the first coming from Sam Reinhart 5:13 into the game and another when Jeff Skinner hit iron at the 6:50 mark - before Washington took a 1-0 lead with 2:37 remaining in the opening period while on the power play.
Washington had multiple opportunities to smack the puck in after an Alex Ovechkin blast from the left faceoff circle. Ovechkin pushed his rebound back to the front of the net where Backstrom was able to put it in.
Wilson put the Capitals up 2-0 with a shorthanded goal when he skated in on a 2-on-0, put a move on Ullmark and slipped the puck in on his backhand 6:38 into the second period.
Sheary chipped in a rebound to give the Capitals a 3-0 lead at the 7:28 mark of the third.
Olofsson roofed a shot short side over Vanacek's shoulder to put Buffalo on the board with 8:33 left in regulation. Olofsson's sixth goal of the season was his fifth with the man advantage. He now leads the team in goals and is tied with captain Jack Eichel for the team lead in points (12).
The goal also snapped a 149:47 goal-less streak for Buffalo that dated back to Olofsson's last goal, which came in the second period of Buffalo's game on Monday against the New York Islanders.