The Lightning came from 3-1 and 4-2 down to win with three goals in the third period, two of them from Ryan Malone.
The result leaves the New Jersey Devils, the San Jose Sharks and the Chicago Blackhawks as the league's only unbeaten teams, with the Devils the only one of the trio in action tonight.
They needed overtime to keep their record intact, Ilya Kovalchuk's goal sealing a 3-2 win over the Washington Capitals.
And their Atlantic division rivals the New York Islanders and the Pittsburgh Penguins both suffered 4-2 defeats, to the Boston Bruins and Winnipeg Jets respectively.
Goals from Shawn Thornton, Gregory Campbell, Zdeno Chara and Patrice Bergeron earned Boston victory, Dougie Hamilton starring with two assists, while Keith Aucoin scored twice for the Islanders.
Sidney Crosby's double gave Pittsburgh a 2-0 lead after the first period but Evander Kane, Dustin Byfuglien and Andrew Ladd had a goal and an assist apiece to effect a turnaround for the Jets.
The Carolina Hurricanes beat the Buffalo Sabres for the second night running, coming from behind to win 3-1 with all the goals scored in the third period.
The Detroit Red Wings beat the Minnesota Wild 5-3 after a scoreless first period. Todd Bertuzzi scored twice while Pavel Datsyuk had a goal and two assists.
The Vancouver Canucks beat the Anaheim Ducks 5-0, Mason Raymond scoring twice.