Michael Neuvirth stopped 26 shots for his first shutout of the season, lifting the Capitals to their third win in four games. Neuvirth has five shutouts in his four-year career, with the other four having all come last season.
Ovechkin's wrist shot produced his 10th goal of the campaign.
Ondrej Pavelec took the loss with 27 saves.
Washington hopped past Winnipeg into second place in the Southeast Division, five points behind Florida.