Vincent Lecavalier and Brad Richards had four assists apiece for Tampa Bay. Marc Denis stopped 28 shots.
Dallas got a goal and an assist from Mike Modano. Marty Turco made 29 saves.
Prospal got his second game-tying goal at 9:09 of the second, and Boyle picked up his second power-play goal at 12:25 to put Tampa Bay up 4-3.
Doug Janik made it 5-3 at 1:39 of the third. After Modano cut the Dallas deficit to one at 3:32, Tampa Bay secured the win on goals by Martin St. Louis, on the power play, at 9:48 and Filip Kuba with 6:47 left.
The Stars went up 3-2 at 1:18 of the second on a goal by Janne Niinimaa.
Jussi Jokinen put Dallas ahead 1-0 just 14 seconds into the game.
Tampa Bay scored twice in 21-second span in the first for a 2-1 lead. Prospal tied it at 11:40 before Boyle scored his first power-play goal at 12:01.
Dallas pulled even at 2-2 on Loui Eriksson's goal with 1:21 left in the first.