Lecavalier tied it at 2-all on his 52nd goal at 1:20 of the third. He scored from the low slot off Vinny Prospal's deflected pass. Boyle gave the Lightning a 3-2 lead when skated into the Carolina zone and scored from the right circle at 3:13.
Eric Perrin also scored for the Lightning, who trail Southeast Division-leading Atlanta by one point. Tampa Bay improved to 10-21-1 when trailing after two periods.
Ray Whitney and Rod Brind'Amour had the Carolina goals. The Hurricanes are poised to become the first defending Stanley Cup champion to miss the playoffs the next season since New Jersey in 1996.
Carolina has dropped four of five. It was just the third time in 30 games the Hurricanes have lost when holding a lead entering the third period.