Scott Clemmensen stopped 22 shots for the Panthers and Dan Ellis made 27 saves for the Predators.
Clemmensen got the start in favor of Tomas Vokoun, Nashville's former goalie, who has won just one of his past seven games. Both Ellis and Clemmensen appeared in the only other meeting between the Panthers and Predators this season, a 4-1 Nashville win on Nov. 28, 2009.
Bouillon scored on a shot from the right circle a minute into overtime to give Nashville the win.
Nashville, which was coming off Saturday's 1-0 shootout loss to Detroit, is in fifth place in the Western Conference with 94 points.
The Predators tied the game at 2-2 on Hornqvist's goal with 3:07 left in regulation. Hornqvist scored with a wrist shot that went through Clemmensen's legs.
The Panthers tied the game at 1-1 on Ballard's goal at 3:12 of the third. Weiss and Michael Frolik had the assists on the goal, Ballard's sixth of the season. Weiss then put Florida up 2-1 at 5:53 of the third, when he tipped in Jason Garrison's shot from the blue line. Frolik also assisted on Weiss' goal.
Legwand opened the scoring at 2:41 of the second period with his 11th goal of the season. He took a pass from Colin Wilson and scored on a wrist shot from the top of the right circle.
NOTES: The Panthers recalled RW Victor Oreskovich from Rochester (AHL). Oreskovich replaced RW Byron Bitz in Florida's lineup. Panthers coach Pete DeBoer said Bitz was out with an elbow injury, which occurred Saturday in Ottawa. ... The Predators managed just four shots on goal in the scoreless first period. The Panthers had only six.