The Leafs found themselves 2-0 down two minutes into the second period through goals from Nick Bonino and Mathieu Perreault, but Kessel started the comeback with a powerplay goal at 7:44.
Dion Phaneuf squared things up a few moments later and Kessel completed the turnaround before the end of the second, then sealed his hat-trick in the third.
Brad Richardson netted an overtime winner as the Vancouver Canucks edged out the New York Islanders 5-4.
Chris Higgins put the Canucks ahead for the first time in the game at 4-3 with a goal at the end of the second, but Frans Nielsen tallied with 1:12 left in the third to force overtime.
Martin Erat fired a shootout winner to lift the Washington Capitals to a 5-4 victory over the Winnipeg Jets.
Alex Ovechkin led the Caps with two goals and an assist.
Jonathan Toews scored once in regulation and again in the shootout to help the Chicago Blackhawks overcome the Florida Panthers 3-2.
Josh Harding made 16 saves for his first shutout of the season and goals from Justin Fontaine and Jason Pominville gave the Minnesota Wild a 2-0 victory over the Nashville Predators.
Elsewhere, the Columbus Blue Jackets beat the New Jersey Devils 4-1, the Edmonton Oilers were 4-3 victors over the Montreal Canadiens and the Phoenix Coyotes saw off the Calgary Flames 4-2.