Williams opened the scoring 3:46 into the game. Teravainen made it 2-0 at 4:03 of the second period.
Alex Nedeljkovic started in goal for Carolina and made 14 saves through two periods. Callum Booth made 11 saves in the third.
Lightning forward Adam Erne scored a power-play goal at 15:37 of the second period to make it 2-1.
The Lightning thought they tied the game late in the third period on a goal by Alexander Volkov, but it was waved off because of goalie interference.
Michael Leighton made 20 saves for Tampa Bay. (NHL.com)
The Lightning get Carolina again tomorrow in Raleigh at 7pm.
(Feature Photo/ Christine Gunn)