The Capitals (6-4-3) won for the second time in their past five games (2-2-1) and ended the Oilers' five-game road winning streak.
Forward Connor McDavid extended his points streak to eight games (six goals, five assists) with a first period power-play goal for Edmonton (8-5-1), which had won two straight and five of its previous six games.
"We needed that win and we knew they have a pretty good team," Ovechkin said. "Obviously, I think tonight the fourth] line set the tone."
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The fourth line of Jakub Vrana, Travis Boyd and Devante Smith-Pelly scored goals on its first two shifts to stake Washington to a 2-0 lead. Smith-Pelly had a goal and an assist, Vrana scored a goal, and Boyd had two assists. Defenseman John Carlson also had two assists.
Capitals backup goalie Pheonix Copley made 31 saves to earn his second win of the season. Cam Talbot made 19 saves for Edmonton.
"I think it was a team effort," said Copley, who made his first home start. "Everybody kind of buckled down. We talked about game management. I think we did a good job of that tonight."
The Capitals focused on their defense after losing their previous two games (0-1-1). Although McDavid scored a power-play goal, the Capitals held him in check for most of the game, limiting him to two shots on goal, one at even strength, and none over the final two periods.