Kadri's goal gave the Maple Leafs a 5-2 advantage, after which Daniel Alfredsson and Colin Greening scored for the Senators.
Ottawa came up short, however, and slipped to 0-2-2 on its current five-game road trip. Toronto won its third straight.
After Ottawa cut its deficit to 3-2 early in the third, Phil Kessel and Kadri rebuilt Toronto's three-goal cushion.
James Reimer faced 43 shots and stopped 39 of them to get the victory. All five Toronto goals were scored against Ben Bishop on 28 shots.
Swim Week Miami Beach 2014 [PHOTOS]