Milan Lucic and Patrice Bergeron both lit the lamp in the third period to bring the Bruins even, but after Boston failed to score on a power play that stretched into overtime, the Leafs capitalized on their chance on the man- advantage.
With Boston's Torey Krug in the box for holding, Cody Franson fed the disc from the left point to the low left side, where Kadri roofed a shot over Chad Johnson to send Toronto to its second straight victory.
Paul Ranger, James van Riemsdyk and Tyler Bozak each scored once for the Leafs, who kept pace with Columbus for the final wild-card spot in the Eastern Conference. The Blue Jackets, who blanked Philadelphia on Thursday, have 85 points, giving them a one-point lead over the Leafs with two games in hand.
Jonathan Bernier made 25 stops over two-plus periods for Toronto before leaving the game with 11:38 remaining in regulation after Bergeron landed awkwardly on top of his left leg. James Reimer stopped 10-of-11 shots in relief.
Brad Marchand recorded Boston's other marker, while Johnson stopped 27 shots in the Bruins' second straight setback.