Lecavalier gave the Lightning a 3-2 lead with 5:06 left in the third period from the top of the right circle during a power play. Vinny Prospal had an empty-net goal at 19:11 to make it 4-2.
Steven Stamkos pulled Tampa Bay even at 2 from the low slot off a pass from Steve Downie at 11:46 of the third.
Brad Richards and Loui Eriksson scored for the Stars, who had their eight-game winning streak at Tampa Bay snapped. It was Dallas' first loss at Tampa Bay since Feb. 19, 1996.
Dallas, with the NHL's worst road power play, converted one of six man-advantage situations through two periods. Tampa Bay had just one power-play chance during the stretch, coming with 3:01 left in the second.
The Stars are 8-4-3 in their last 15 games.
The play at the Florida Panthers Wednesday night.