Alex Semin and Eric Staal both scored in the second period but the Lightning has a 5-2 lead.
Semin scored twice Saturday as the Canes edged the Florida Panthers 3-2. His goal Sunday came on the power play as the winger skated through some flat-footed Bolts and winged a shot past Bishop.
Staal then made a 4-2 game, swiping the puck from defenseman Jean-Philippe Cote in the neutral zone, skating down the right wing and beating Bishop.
A comeback appeared to be brewing, but not for long. Tampa Bay’s Mark Barberio scored his second goal of the game on a shot from the top of the left circle, pushing Tampa Bay's lead to 5-2.
The Lightning, which has won eight of the last nine games at PNC Arena, knocked Canes goalie Justin Peters out of the game in the first.
Despite being outshot 17-8 in the opening period, the Lightning took a 3-0 lead, getting goals from Barberio, Ondrej Palat and Nikita Kucherov. Goalie Ben Bishop, who has twice shut out the Canes at PNC Arena in his career, has turned back every threat.
The Canes had an 8-1 shooting edge when center Riley Nash was penalized for tripping at 4:42. Barberio scored his first NHL goal with an easy backdoor tap-in. After the Canes' Andrej Sekera broke his stick, forward Pat Dwyer gave him his stick and skated to the bench for a new one, leaving the Bolts with a 5-on-3 advantage.
Palat scored his 10th of the season with 12:28 left in the first off a perfect pass off the rush from Martin St. Louis. Kucherov's goal came after he hopped on a loose puck in the Canes zone.
That was it for Peters, who left with 4:53 left in the period as Anton Khudobin came in. Peters was making his first start since Dec. 27.
Bishop's biggest stop may have been among the first. During an offensive flurry by the Canes, Jeff Skinner was looking to bang in the puck at the post but Bishop moved quickly to make the save 70 seconds into the game.
The Canes had two power plays in the opening period but could get anything past the 6-foot-7 Bishop, who blanked the Canes 3-0 on Nov. 1 at PNC Arena.
One milestone for the Canes: center Manny Malhotra is playing his 900th career game.