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.