Alex Ovechkin scored his NHL leading 33rd goal of the season in the opening period, but it took a comeback in the final 20 minutes to bring the Capitals their second straight win.
Phil Kessel put Toronto in front 2-1 just 54 seconds into the third, but Backstrom tied it at the 4:36 mark.
The game-winner came on a wrist shot by Ward with 8:09 to play.
Toronto suffered its fourth straight loss with Jonathan Bernier giving up the third-period goals and making 32 saves.
Michal Neuvirth stopped 32 shots in the victory, which moved Washington into a second-place tie with Philadelphia in the Metropolitan Division.
2014: The Year in Music [PHOTOS]