Cody McLeod gave the Predators a 2-0 lead at 15:19 of the first period. Patrick Marleau scored for the Sharks to make it 2-1 at 4:24 of the second period on the power play.
"We're giving up some goals," San Jose coach Peter DeBoer said. "It's a combination of things, I think. Obviously it's not good enough to win games, so we've got to figure it out and I don't have an answer standing here for you, but I know our group. Every team I've ever coached has a tough part of the season, and this is obviously ours."
Neal gave the Predators a 3-1 lead with a power-play goal at 4:48, and P.K. Subban made it 4-1 at 14:39.
Sissons' second goal of the game gave the Predators a 5-2 lead at 5:27 of the third period on a redirection of a shot by Craig Smith.
"He can finish and score a lot of goals," Wilson said. "He's playing hard, he's getting on the forecheck. [Smith] and [Sissons] have been forechecking those [defensemen] really hard and turning pucks over, so he's doing that and getting to the net."
Neal made it 6-2 at 17:01 of the third period on the power play. It was his second goal of the game and 23rd of the season. Viktor Arvidsson made it 7-2 with 38 seconds remaining.