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.