Joffrey Lupul also scored and added three assists for the Leafs (20-12-4), while Kadri also picked up an assist as Toronto won its third straight game extended its point streak to eight games.
Ben Bishop made 19 saves for the Senators (19-10-6), who were coming off a 3-0 shutout over the New York Rangers on Thursday.
The Leafs led 1-0 after the first period and 2-0 after the second before Kadri scored twice in the opening five minutes of the third period to complete his hat trick.
The first of those goals came at 2:44 of the third after a horrible giveaway as Senators forward Jakob Silfverberg tried to clear the puck but instead gave it right to Lupul leading to a two-on-none in front of Bishop. Lupul fed a pass to Kadri at the side of the goal and he deposited it into a wide open net.
Lupul then set up Kadri for a one-timer that beat Bishop at 4:48. The resumption of play was delayed as hats littered the ice in appreciation of Kadri's efforts as a visiting player. The pro-Toronto crowd in Ottawa broke into chanted his name in the ensuing minutes.
The second period produced just one goal, by Kadri on a delayed penalty call at 12:15, and four minutes in penalties, two delay of game calls against the Leafs.
That was a stark contrast to the first period. Lupul scored a power-play goal, but there were 40 minutes in penalties, including six fighting majors. Lupul now has eight goals in his last six games since missing 25 with an injury.
Matt Kassian was the busiest player in the first as he took on both Colton Orr and Frazer McLaren. Colin Greening and Mark Fraser were the other combatants.
The Leafs also held an 11-5 edge in shots over the opening 20 minutes, but the Senators turned the table in that department during the second period as they outshot the Leafs 12-6 .
Ottawa held a 31-23 advantage in shots overall.
Notes: Clarke MacArthur and Jake Gardiner were scratches for Toronto. Mike Lundin and Peter Regin were the Sens' healthy scratches for the second straight game ... Going into Saturday, the Leafs led the NHL in hits with 1,143, blocked shots with 590 and fighting majors 34, a number they increased by three in the first period ... The Senators remain just one of four teams (New York Islanders, Los Angeles Kings, Minnesota Wild) that have yet to allow a short-handed goal this season ... The loss was just the third in regulation on home ice for the Senators in 19 games this season ... Ottawa is 49-37-3-5 all-time against the Leafs including 26-15-5 at home.