Joffrey Lupul scored and had two assists for Toronto, which tallied the game's first four goals and held a 5-1 lead shortly into the third period. But three consecutive Senators scores made it a tight game.
Kessel provided some breathing room with 2:19 to play -- a necessary score, given Ottawa rookie Stephane Da Costa recorded his first career goal only 25 seconds later.
But Toronto held on in the wild finish to stay unbeaten. The Leafs opened their season Thursday with a 2-0 victory against Montreal.
James Reimer made 32 saves in that shutout win and was strong through two periods Saturday, stopping all 16 shots he faced. But he was peppered with 16 shots in the third and let in all five goals.
Craig Anderson, Ottawa's starting goaltender, gave up four goals on 24 shots through two periods. Alex Auld allowed two goals in the third period as the Senators' comeback effort fell short, dropping them to 0-2-0. They lost Friday at Detroit to start their 2011-12 season.