Teravainen tied it 1-1 with a power-play goal at 9:56 of the third period. Trocheck made a cross-crease pass to Teravainen, who was open for a backdoor goal.
"[Vasilevskiy] is a great goalie, we know that, everybody knows that," Teravainen said. "He played a great game. We've just got to put the pucks at him and create some traffic."
Carolina had a 5-on-3 advantage for 1:34 in the second period and failed to score despite Vasilevskiy being without a skate blade for almost a minute after Teravainen's shot knocked it off.
"You don't see that very often," Teravainen said. "I didn't know the rule ... if they were going to whistle the game down or just keep going. Everybody just tried to create something, do something and got a little confused."
The Lightning were 0-for-4 on the power play and are 3-for-28 since losing forward Nikita Kucherov to a lower-body injury on Oct. 16.
"That was arguably the difference, our [penalty kill] was outstanding, especially to get through that 5-on-3 for as long as we did," Tampa Bay coach Jon Cooper said. "But you give a power play like that 8 1/2 minutes of time you're flirting with danger.
"The problem is we had seven minutes of power-play time and I think we had one shot on goal. Our power play most definitely needs to be better."
NOTES: Lightning defenseman Erik Cernak left the game in the first period with an upper-body injury. Cooper said he expects Cernak to miss a few games. ... Lightning forward Alex Killorn had an assist and has scored eight points (four goals, four assists) in the past six games. ... Hurricanes defenseman Tony DeAngelo had an assist on the game-winning goal. He has scored seven points (two goals, five assists) in the past six games. ... Hurricanes center Andrei Svechnikov had an assist and has scored a point in all but one game (15 points; seven goals, eight assists). ... Trocheck has scored six points (one goal, five assists) in the past six games.