The Lightning and Hurricanes opened the season against each other after meeting in the final regular-season contest last year. Tampa Bay won that contest 6-2 and knocked Carolina out of playoff contention.
Tampa Bay went on to reach the Eastern Conference finals before falling in seven games to Stanley Cup champion Boston.
The Tampa Bay lead was only 2-1 as the game reached the midway point of the third period, but Downie tipped in a shot on the power play with 7:38 to play and Hall scored on a wrist shot 10 seconds later.
Ryan Malone added a goal with 2:12 remaining.