Jeremy Lauzon had a goal and an assist, and Juuse Saros made 27 saves for the Predators (30-25-2), who have won three in a row.
“We understand where we are in the standings and where we are in the season, and points are so crucial,” Sissons said.
Kevin Fiala scored, and David Rittich allowed two goals on 19 shots for the Kings (28-17-10), who had their four-game winning streak end.
“Give them credit, they made it difficult,” Los Angeles interim coach Jim Hiller said. “And so your execution has to be even a little bit better when you’re playing a team that checks you that well, and ours wasn’t, so that made it doubly hard.”
Yakov Trenin gave the Predators a 1-0 lead at 8:47 of the first period. He got a step on Adrian Kempe and received a pass from Sissons in the left circle before sliding a backhand in off the diving glove of Rittich.