Kadri, who scored Toronto's second power-play goal late in the first, tied it at 3 with an unassisted goal 14:10 into the third after the Maple Leafs allowed three straight goals to blow a 2-0 lead.
He drew an assist when Kessel put Toronto ahead to stay with his fifth goal at 18:10. Nikolai Kulemin also scored his fifth goal in the first and Jean-Sebastien Giguere stopped 22 shots for the Maple Leafs, who improved to 4-3-1.
Milan Michalek and Chris Campoli scored in the second and Daniel Alfredsson gave Ottawa a 3-2 lead early in the third.
Pascal Leclaire made 15 saves for Ottawa, which fell to 2-4.
The chippy encounter between the provincial rivals included a fight between Ottawa's Alex Kovalev and Maple Leafs defenseman Francois Beauchemin midway through the second.
Kulemin put a backhand past Leclaire to open the scoring 8:08 in. Kadri made it 2-0 with Toronto's second power-play goal of the period at 19:23.
Michalek drew the Senators within one midway through the middle period, snapping a shot past Giguere from a sharp angle, low in the right faceoff circle.
Campoli tied it at 2 late in the second. The Ottawa defenseman's shot from the left point got past Giguere at 17:10 as Toronto captain Dion Phaneuf battled with Nick Foligno in the goalmouth.
Alfredsson gave Ottawa its first lead 1:06 into the third when he took Campoli's centering pass from behind the net and snapped a shot past Giguere.
|8:08||Power Play - Nikolai Kulemin - Assist: Luca Caputi|
|19:23||Power Play - Nazem Kadri - Assists: Francois Beauchemin and Tomas Kaberle|
|9:12||Milan Michalek - Assists: Jared Cowen and Matt Carkner|
|17:10||Chris Campoli - Assists: Nick Foligno and Zack Smith|
|1:06||Daniel Alfredsson - Assists: Chris Campoli and Jason Spezza|
|18:10||Power Play - Phil Kessel - Assists: Dion Phaneuf and Nazem Kadri|
|3:00||Jay Rosehill: fighting - major|
|3:00||Francis Lessard: instigator - minor|
|3:00||Francis Lessard: fighting - major|
|3:00||Francis Lessard: misconduct - misconduct|
|5:35||Tim Brent: roughing - minor|
|5:35||Milan Michalek: roughing - minor|
|7:39||Jason Spezza: slashing - minor|
|9:55||Colby Armstrong: roughing - minor|
|9:55||Cody Bass: roughing - minor|
|9:55||Bobby Butler: hooking - minor|
|18:34||Zack Smith: hooking - minor|
|19:54||Fredrik Sjostrom: hooking - minor|
|2:59||Zack Smith: goaltender interference - minor|
|4:51||Korbinian Holzer: roughing - minor|
|4:51||Matt Carkner: roughing - minor|
|5:40||Fredrik Sjostrom: tripping - minor|
|6:39||Sergei Gonchar: hooking - minor|
|9:56||Francois Beauchemin: fighting - major|
|9:56||Jay Rosehill: roughing - minor|
|9:56||Jay Rosehill: interference - minor|
|9:56||Alex Kovalev: fighting - major|
|9:56||Mike Fisher: high-sticking - minor|
|14:06||Luca Caputi: roughing - minor|
|14:06||Zack Smith: roughing - minor|
|18:50||Korbinian Holzer: holding - minor|
|4:03||Nick Foligno: holding - minor|
|9:54||Bobby Butler: elbowing - minor|
|14:45||Tim Brent: tripping - minor|
|16:47||Mike Fisher: holding - minor|
|Shots on Goal|
|Attendance - 15088|
|Referees - Marc Joannette, Jean Hebert|
|Linesmen - Derek Nansen, Mark Shewchyk|