Kadri scored twice in just over a 2-minute span of the third period to help the Maple Leafs take control and roll to their fourth win in five games.
James Reimer posted his second shutout of the season with 31 stops, and Joffrey Lupul added a goal and three assists, giving him eight goals and five assists in six games since returning from a broken forearm.
The win allowed Toronto to pull into a tie with the Senators for the fifth Eastern Conference playoff spot.
Ben Bishop yielded four goals on 23 shots as Ottawa fell for the just the second time in eight contests.
Notable deaths of 2014 [PHOTOS]