With the scored tied 1-1 midway through the period, Nicklas Backstrom held the puck on the right side of the net and fired a pass through the crease that found an unchecked Ward for the one-timer, his first goal of the season.
Backstrom finished with three assists and Ovechkin also contributed a helper for Washington, which notched just its second win in six games starting the season.
Braden Holtby turned aside 28-of-30 shots in the victory.
Boyd Gordon and Will Acton each found the net for the Oilers, who dropped a third straight.
Jason LaBarbara made 16 stops for Edmonton.