Kucherov made it 2-1 with a one-timer from the hash marks at 5:28 of the second period after Cirelli eluded two defenders to dig the puck out of the corner.
"I think we are battling hard right now, starting from [Vasilevskiy] all the way out, and [he] made some big stops for us tonight," Cirelli said. "And working our way out, the [defense] is blocking some shots, getting in lanes, moving it up to the forwards and getting pucks in deep and being able to skate."
Rakell tied it 2-2 at 7:57 with a goal a few seconds after the Ducks dominated zone time on a power play.
Point gave Tampa Bay a 3-2 lead with a power-play goal at 12:39, and Pat Maroon made it 4-2 at 14:25 of the second.
Cirelli scored a power-play goal at 6:20 of the third period to make it 5-2. It was his fourth straight game with a goal.
"Sometimes you get lucky and pucks go in for you," Cirelli said. "But more importantly, anything you can do to help the team win, and right now we are all going."
Palat reached his milestone with a power-play goal at 17:28 for the 6-2 final.