Stastny signed a one-year, $1.5 million contract with the Hurricanes on Aug. 23; Coghlan was acquired with forward Max Pacioretty in a trade with the Vegas Golden Knights on July 13.
Andrei Svechnikov had a goal and an assist, Jesperi Kotkaniemi had two assists, and Frederik Andersen made 20 saves for Carolina.
Vladislav Namestnikov scored, and Maxime Lagace made 41 saves for Tampa Bay.
Svechnikov (11:50) and Stastny (15:46) each scored a power-play goal in the second period when the Hurricanes opened a 2-0 lead.
Sebastian Aho made it 3-0 at 4:57 of the third period, and Seth Jarvis extended the lead to 4-0 off a pass from Svechnikov at 6:29.
Namestnikov cut it to 4-1 at 11:42, but Malte Stromwall scored on the power play at 18:23 for the 5-1 final.
The Hurricanes went 3-for-5 with the man-advantage; the Lightning were 0-for-2.
The Lightning announced Monday that they were postponing their preseason games against the Hurricanes on Wednesday and the Nashville Predators on Thursday at Amalie Arena in Tampa because of the potential effects of Hurricane Ian. They will instead play the Predators at Bridgestone Arena in Nashville on Thursday.
