The 22-year-old from London, Ont., scored a one-timer on Ottawa's Ben Bishop at 4:48 of the third period to complete his hat trick. Resumption of play was delayed as hats littered the ice and chants of "KA-DRI" broke out.
"Leafs Nation is everywhere," said Kadri. "We obviously appreciate the support and want to give back as much as we can. To see everyone, especially at the start of the game with that 'Go Leafs Go' chant, and to hear it throughout the whole building, it kind of got everyone going. We took advantage of that."
Joffrey Lupul scored and added three assists for the Leafs (20-12-4), who have won three in a row and continued an eight-game point streak.
Bishop made 19 saves for the Senators (19-10-6), which was coming off a 3-0 shutout over the New York Rangers on Thursday.
"We thought it was going to be a lot closer," said Senators forward Zack Smith. "We're used to playing tight games.
"It was 4-0 but I don't think it was a 4-0 game. We had a lot of chances, just maybe not the quality third and fourth chances that we're used to scoring on."
The Leafs led 1-0 after the first period and 2-0 after the second.
"I think we had a great start, and that's one of the things we've been focusing on. Any time you can get a decent start on the road, it puts more pressure on the home team to perform," said Toronto head coach Randy Carlyle.
The first of Kadri's goals came at 12:45 of the second after a horrible giveaway as Senators forward Jakob Silfverberg tried to clear the puck but instead gave it right to Lupul leading to a 2-on-0 in front of Bishop. Lupul fed a pass to Kadri at the side of the goal and he deposited the puck into a wide-open net.
Lupul took advantage of another Senators' giveaway to setup Kadri again for the game's final goal.
The Senators appeared to score in the third period as Erik Condra tucked a loose puck in from beside the post, but the referee had blown the play dead.
Senators coach Paul MacLean said whether it was in or not was irrelevant as they didn't score any others. When asked what went wrong for his team, MacLean said giveaways would be a good place to start.
"Two of them right in front of your net in the third period makes it kind of hard for your goaltender to save you," said MacLean. "That little bug-a-boo that we've had in the past about execution in came back to bite us.
"I don't know if Toronto had better puck luck that we did but at the end of the day they ended up playing better than we did and they win."
The second period produced just one goal, by Kadri on a delayed penalty call at 12:15. There were also just four minutes in penalties, two delay of game calls against the Leafs, which was a stark contrast to the first period.
The opening 20 minutes also produced just a single goal, a power-play effort from Lupul, but there were 40 minutes in penalties, including six fighting majors.
Ottawa's Matt Kassian was the busiest player in the open period as he took on both Colton Orr and Frazer McLaren in fights. The Senators' Colin Greening and Toronto's Mark Fraser were the other combatants.
"They put the puck in the net and we didn't. Reimer made some good saves and they got a couple bounces that helped them out too, but we just weren't good enough from the drop of the puck and they wanted it more," Kassian said.
"I don't think we got pushed around or got dominated physically. We just got outworked, outskilled and outplayed. That's the bottom line."
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 in the second.
Ottawa held a 31-23 advantage in shots overall.
Notes: Clarke MacArthur and Jake Gardiner were scratches for Toronto Saturday. Mike Lundin and Peter Regin were the Ottawa healthy scratches for the second straight game…With his goal Saturday, Lupul has eight goals in his last six games since missing 25 with an injury…Going into Saturday the leafs led the NHL in hits with 1143, 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 against this season…The loss was just the third in regulation on home ice for the Senators in 19 games this season…The Senators are 49-37-3-5 all-time against the Leafs including 26-15-5 at home.