Second-year centre Ryan Craig scored Tampa Bay's first two goals, including the tying goal about two minutes into the third period. Tampa Bay edged Atlanta and the Toronto Maple Leafs by two points for the Eastern Conference's final playoff spot last season.
Denis, who came to Tampa Bay in a trade with Columbus, struggled in the opening period allowing two goals on six shots.
Denis denied Slava Kozlov, Jon Sim and Ilya Kovalchuk in the shootout.
Lecavalier, the first shooter for the Lightning, beat Kari Lehtonen with a shot to the right edge of the net. Brad Richards was stopped by Lehtonen on Tampa Bay's second and final shot of the shootout.
The Thrashers, who must replace the scoring lost with the departures of forwards Marc Savard and Peter Bondra, were outshot 24-10 in regulation and 26-11 through the overtime.
Lehtonen, limited by injuries to only 38 games last season, proved his return to health by stopping 24 shots through overtime.
Scott Mellanby and Marian Hossa scored first-period power-play goals for the Thrashers.
Lehtonen's 2005-06 troubles began when he suffered his first groin injury in the first period of the season opener. He survived the season opener Thursday night.
Atlanta, which led the league with 58 power-play goals last season, was back in business with the advantage early. Mellanby's first goal on a slap shot came only nine seconds after Tampa Bay's Nikita Alexeev drew a minor penalty for hooking.
Mellanby tipped in a pass from Hossa for the goal. The delicate shot was hit with so little force it barely reached the back of the net.
Less than six minutes later, the Thrashers took advantage of a 5-on-3 advantage by patiently making several passes before Hossa took a pass from Mellanby across the front of the net and scored from the right edge for a 2-0 lead with about seven minutes left in the period.
The Lightning answered with a power-play goal four minutes into the second period. Craig tipped in Richards' long shot from between the circles.
Notes: Thrashers D Braydon Coburn opened the season on the injured list after hurting his shoulder in a pre-season game at St. Louis on Sept. 24. ... The Lightning won last season's series with the Thrashers 4-3-1. ... Atlanta faces Southeast Division opponents in nine of its first 10 games. ... Craig tied for the Tampa Bay lead with eight points in the pre-season. ... Thrashers D Steve McCarthy was credited with two assists.