Kucherov made it 3-1 with a power-play goal at 19:40.
Carrier scored to make it 3-2 at 10:42 of the second period after a pass through the crease from Philip Tomasino.
Stamkos extended the Lightning lead to 4-2 at 13:58 with a goal off a one-timer from below the left face-off circle.
Ross Colton made it 5-2 at 1:37 of the third period with his fifth goal in the past three games and Pat Maroon scored at 2:08 to make it 6-2.
Saros was pulled for David Rittich, who made nine saves in relief.
"We're trying to amp up our game here," Cirelli said. "We've had a couple of big, emotional games in the past week. We know what playoff hockey is like and I think it's just us gearing up and getting ready."
NOTES:Stamkos has scored 13 points (three goals, 10 assists) during a five-game multipoint streak, including three straight with three points. ... Stamkos (35), Brayden Point (27), Alex Killorn (25), Colton (22) and Kucherov (21) also have scored 20 goals for Tampa Bay. ... Kucherov has scored 11 points (six goals, five assists) during a five-game point streak. ... Boyle scored 20 goals for the Lightning in 2006-07. ... Lightning forward Pierre-Edouard Bellemare did not play because of a lower-body injury and is day to day. ... Point got his 200th NHL assist on Kucherov's goal. ... Predators forward Matt Duchene had an assist and has scored four points (two goals two assists) during a four-game point streak.