"Last game we had a shootout, he was just looking at me with those eyes," Tampa Bay coach Guy Boucher said. "Usually, whatever league I was in, I always choose those guys. They want it, and it usually works out."
Hedman has scored two goals in 30 games this season. The defenseman's goal was the lone one in the shootout.
Smith played in his first game since allowing five goals on 22 shots over 41 minutes of an 8-1 loss to the Boston Bruins on Dec. 2.
"I felt prepared," Smith said. "I've been working this past week on fundamental stuff. I just went in there and said, 'Play your game.' I was much more relaxed."
Sean Bergenheim scored for the Lightning, who have beaten the Thrashers eight straight times.
Rich Peverley had the lone goal for the Thrashers.
"We're pleased we only gave up a goal, but our goal is to score," Atlanta coach Craig Ramsay said. "We had some opportunities and we didn't cash them in. When you're presented with some chances to score, you've got to get it done."
The Thrashers went 0-for-5 on the power play. Tampa Bay failed to score on its two man-advantage opportunities.
Tampa Bay Lightning captain Vincent Lecavalier returned after missing 15 games because of a right hand injury. The center, injured at Washington on Nov. 11, had surgery four days later to insert a plate and screws to secure an unstable fracture.
"I felt really good," Lecavalier said. "I thought my legs would be tired in my first game back, but I had a hop in my skating."
Peverley scored Atlanta's sixth short-handed goal of the season for a 1-0 lead at 13:56 of the first period. Thrashers goalie Ondrej Pavelec stopped a pair of in-close shots by Lecavalier during the frame.
Bergenheim tied at 1 with 5:42 left in the second right after he served a high-sticking penalty. He beat Pavelec to Randy Jones' clearing pass into the right circle and scored after the goalie's poke check bounced off Bergenheim's skate and wound up near the forward's stick.
Pavelec finished with 30 saves. He is winless in seven career shootouts.
"That was a really tight game," Lecavalier said. "Both goalies played great."
Lightning center Steven Stamkos, who has 24 goals and 20 assists, didn't record a point. He had five goals and two assists in two previous games this season against Atlanta.
Tampa Bay has allowed seven short-handed goals. Six were scored in the Lightning's 12 home games, tying the franchise record for most allowed at home in one season. ... The Thrashers were outscored 10-5 in losing twice to Tampa Bay this season. ... Lightning left winger Ryan Malone had a seven-game point streak (four goals, six assists) snapped. ... Atlanta center Bryan Little had scored in three straight games.