It was the second straight shutout for Reimer, who blanked Pittsburgh, 1-0, on Wednesday.
"It's obviously a lot of fun," Reimer said. "I wish I could take credit for it, but the guys played unbelievable tonight. Our D-men played great, boxing guys out."
Craig Anderson made 35 saves on 40 shots for the Senators, who have dropped a season-high six straight.
"This is definitely the worst loss, it's against a big rival, a team we're battling with," Senators center Jason Spezza said. "You hope this is the end of this."
Kessel gave Toronto the only goal it needed with 6:13 to play in the first as he skated into the Ottawa end through the middle, snapped a shot on net that was stopped and banged in his own rebound for his 27th goal of the season.
It was a 2-0 game just over three minutes later when Kessel sent a pass from the left point to the right circle where Phaneuf quickly gathered the puck and slapped it in.
The Leafs took a 3-0 lead at the 8:25 mark of the second as Bozak received a lead pass from Kessel and got down low before chipping the puck over a sprawled out Anderson.
Reimer made 12 saves in the first period and stopped 21 in the second to keep Ottawa off the board.
Luke Schenn made it a 4-0 game 5:39 into the third with his second of the year while Franson scored with 7:43 to play to account for the final score.
Reimer has six shutouts over his two years in the NHL...Toronto hosts Edmonton on Monday...The Senators welcome St. Louis to Ottawa on Tuesday...Ottawa has won three of the five games against Toronto this season.