Austin Watson and Sissons had fired Nashville into a 2-0 first period lead but Ondrej Kase pulled one back in the second period to make it 2-1.
Sissons grabbed a second to make it 3-1 before Chris Wagner and Cam Fowler scored for Anaheim to tie it at 3-3.
But the Anaheim fightback was the cue for a decisive burst of scoring that began when Sissons smashed in a one-timer from the left circle after good work by Calle Jarnkrok.
Filip Forsberg and Watson then applied the coups de grace, scoring into an empty net to make it 6-3.
Nashville coach Peter Laviolette lavished praise on hat-trick hero Sissons after a win that he said came after a year of hard work.
“Colton’s answered all the challenges that we’ve asked of him lately, and tonight, I think, his game tonight went to another level,” Laviolette said.
“The goals are one thing, but the way he competed, the way he defended, the penalties he killed, the faceoff battles he got into. The hits that he took, the hits that he gave, he was — that’s the best I’ve seen him.”
Sissons meanwhile described his three-goal blast as the latest stop on a season that had been a “wild ride,” which has seen him drift in and out of the Predators starting line-up.
“It was a wild ride so far this year, a lot of challenges for me personally, obviously being out of the lineup. I just wanted to be a regular guy playing every single night. But it feels good and I’m just enjoying it,” Sissons said.
“I’m not going to lie. Obviously I don’t think I even dreamt this moment, scoring a hat trick in a Western Conference-clinching game.”
Laviolette said his team would be allowed to savour the moment before turning attention to the finals.
“Our guys fought incredibly hard through the course of the year to try and get better, to get ourselves in a position to make the Playoffs and then certainly fought hard in the Playoffs,” he said.
“Our guys know the big picture. They understand what it is that we’re trying to do here. And when that time comes, we’ll be ready. But tonight they’re going to enjoy the fact that they just won a game and they’re moving on.”
Nashville now face either the Ottawa Senators or the Pittsburgh Penguins in the finals, which get under way on May 29 in the Eastern Conference venue. Goalie Pekka Rinne also had another strong night for Nashville, making 38 saves.
Anaheim outshot the Predators by 41-18 and dominated the closing stages.
But Nashville’s sharper eye for goal proved decisive. Ducks goalie Jonathan Bernier, in for the injured starter John Gibson stopped only 12 of the 16 shots he faced.