Kessel scored with 5:48 left in regulation and Toronto escaped the Sommet Center with a 4-3 win over the Nashville Predators despite letting the three-goal lead it built after one period slip away.
The Predators outshot the Leafs 22-11 over the final 40 minutes and erased their deficit on goals by Marcel Goc, Cody Franson and Ryan Jones.
But Kessel capitalized with a wrist shot that beat Dan Ellis, and Toronto goalie Jonas Gustavsson withstood the Nashville attack the rest of the way to finish with 27 saves.
"It was a huge goal for our hockey club," center Matt Stajan said. "Playing with Phil during this stretch he was pressing. He was trying his best to score that goal and get rolling again.
"It was big goal for him and the team. We know he is going to get his fair share of chances. Hopefully, this will get him rolling."
Alexei Ponikarovsky had a goal and an assist in the opening nine minutes and the Leafs also received scores from Niklas Hagman and Stajan in building a quick 3-0 lead on the road.
"We've got to learn from this," Nashville captain Jason Arnott said. "We know we are losing at home and we've got to change it quick. We played well on the road and then we come home and it takes us two periods to get going. By that time we were too far behind."
Predators goalie Pekka Rinne was pulled after facing just eight shots and replaced by Ellis, who seemed to stabilize his team. Goc got them on the board with 2:22 remaining in the second period, controlling the puck after it deflected off the stick of teammate J.P. Dumont and putting a backhander past Gustavsson.
Nashville really turned it on in the third, holding a 13-5 shots advantage. Franson’s one-timer at 4:21 made it a one-goal game, and Jones evened the score 1:58 later by tipping in the puck after Nick Spaling’s shot from just inside the blue line deflected off a stick in front.
"I thought Ellis was the star of the game," Predators coach Barry Trotz said. "Ellis made two or three big saves. Toronto could have run away with the game."
Early on it didn’t look like the Leafs would have any trouble gaining two points out of this game. Hagman needed just 2:02 to give them the lead with a shot that beat Rinne between the pads.
Ponikarovsky followed at 5:12 with a backhander that bounced off Rinne and into the net, and Stajan forced the goalie switch at the nine-minute mark when he scored on another backhander from the low slot.
"I saw Nashville cheating on a change and I kind of had some speed," Stajan said. "Tomas Kaberle is one of the best puck moving defensemen in the league. I knew Kaberle was coming to me and he sprung me. It was a great play by him."
Toronto had to sweat this one out, but with three more stops remaining on a five-game road trip, the most important thing to coach Ron Wilson was the end result.
"We really persevered," Wilson said. "We hope we can turn this into something, but we have a tough week ahead with three more road games."
Material from wire services was used in this report.