Ovechkin gave Washington a 1-0 lead less than 8 minutes into the game when he took a pass from Kari Alzner at the point, skated in alone on Anders Lindback and fired the puck low to the glove side for his 11th goal of season.
Backstrom doubled the advantage with a wraparound tally 8 minutes later and the Caps went on to even their record under new head Coach Dale Hunter at 5-5-0.
Alexander Semin and Troy Brouwer also scored while Michael Neuvirth had to make only 20 saves to get the victory.
Sergei Kostitsyn scored and Lindback stopped 19-of-23 shots for the Predators, whose five-game winning streak came to an end.
Notable deaths of 2014 [PHOTOS]