TAMPA, Fla. -- Ryan Miller kept Buffalo in the game and his teammates took advantage of it.
Miller made 24 saves to remain undefeated (6-0-1) in regulation this season. He didn't allow a shootout goal.
Myers beat Lightning goalie Mike Smith after making several stickhandling moves.
"I guess the coaches felt something," the 6-foot-8 rookie defenseman said. "I'm happy I backed them up on it."
Stafford got the Sabres even at 2 with 16.1 seconds remaining in regulation with Miller on the bench for an extra skater.
"We were able to get the lucky bounce there at the end," Stafford said.
Vincent Lecavalier stopped a personal 15-game goal-scoring drought and Steven Stamkos scored early in the third period for Tampa Bay, which is 0-3 in shootouts this season.
"It's really getting frustrating, the shootout," Tampa Bay coach Rick Tocchet said. "This team is still learning how to win. That's a tough loss for us. You learn from your mistakes and move on."
Lecavalier just missed scoring in the fourth round of the shootout.
"I got a little fortunate," Miller said. "I got enough of it to knock it into the crossbar. It had all the makings of going into the net. It was high enough on the crossbar to stay out."
Mike Grier also scored for the Sabres.
Lecavalier put the Lightning ahead 1-0 on a backhand rebound with six-tenths of second left in the first. It was the Tampa Bay captain's first goal since March 17 against Toronto.
Tampa Bay went up 2-1 at 4:26 of the third when Stamkos stole the puck behind the Buffalo net and scored on a wraparound. He has seven goals over his last seven games.
"Once we got that lead, we kept pressing and didn't give them much," Stamkos said. "They throw pucks to the net and they seem to find their way in. It's frustrating."
Grier tied it at 1 on his 150th career goal from in-close with 44.9 seconds to go in the second. Tim Kennedy setup the goal by stealing the puck deep in the Tampa Bay zone from rookie defenseman Victor Hedman.
Smith made a post-to-post save on Stafford in the first. Miller made a pair of nifty glove saves during the second, one on St. Louis' breakaway and the other when Hedman redirected a shot.
Stamkos has scored a goal in three straight games. He also has five goals and seven points during a five-game point streak.
Martin St. Louis assisted on Lecavalier's goal and has started the season with a nine-game points streak. The right wing has 10 assists and 13 points.
"It's hard to win in this league," Tocchet said. "Nothing comes easy. We've got to keep pounding that into the guys."
Sabres D Toni Lydman (groin strain) didn't play. D Nathan Paetsch replaced Lydman and played for the first time this season. ... Tampa Bay D Paul Ranger was out of the lineup to address a personal matter. ... Lightning D Andrej Meszaros left with an undisclosed upper body injury.