Weber scored two goals, and the Predators routed the Sharks 6-2 on Saturday night.
Pekka Rinne made 32 saves for Nashville and earned his career-high 34th win.
Wilson gave the Predators a 1-0 lead just 2:03 into the game. Jordin Tootoo forced a turnover by defenseman Colin White at the blue line and carried the puck down the ice on the right side. Tootoo sent a pass into the slot to Wilson, who beat Niemi low to the stick side.
Weber doubled the lead 1:20 later.
Sergei Kostitsyn led the Predators into the San Jose zone on a 3-on-2 rush. From the left boards, Kostitsyn passed the puck to Erat in the left circle. Erat found Weber on the right side, and Weber snapped a wrist shot just under the crossbar.
"We came out skating well," Nashville coach Barry Trotz said. "Both the goals were sort of transition goals. We defended well in our end and then we were able to make one quick outlet pass, and away we went. We caught them a little bit on a couple of plays where they were outmanned a little bit."
San Jose coach Todd McLellan called his timeout to try to halt Nashville's momentum.
"Two shots, two goals, two mistakes. Game over," McLellan said. "Pretty simple. We just had a meeting and addressed those two situations in particular, and it came back to bite us."
Marleau brought the Sharks within 2-1 with 9:02 to go in the first, but Klein restored the Predators; two-goal edge five minutes later. Niemi was then replaced by Greiss.
Pavelski scored 23 seconds into the second period to again bring the Sharks within a goal.
"Even though they got that second goal in the first minute of the second period, first shift, those are always the ones you want to keep them out," Rinne said. "It was a good battle from us, and third period they played well and had some chances, but we battled hard and played well defensively."
Joe Thornton had two assists for San Jose, and Marleau and Pavelski both had an assist in addition to their goals. As the Pacific Division leaders, the Sharks entered Saturday in the third spot in the Western Conference, but their loss combined with a win by the Phoenix Coyotes put the Sharks back into seventh place.
"It wasn't a good effort," Thornton said. "We actually made it a game, scoring early in the second period to make it 3-2, but we have to find a way to come together. We're in the seven spot now, and it's unacceptable."
With the Predators on a power play, Weber scored his second of the game with 7:56 to go in the second on a one-timer from just inside the blue line.
"I just tried to stay down on it," Weber said of the rolling puck. "[David Legwand] just kind of one-touched it, and it was rolling. Those are sometimes the hardest ones to shoot."
It was Weber's second two-goal game this season and eighth of his career.
Nashville has scored 44 power-play goals this season, three more than all of last season.
Erat's empty-net goal with 2 minutes remaining, and Spaling's goal in the final seconds of the third concluded the scoring for Nashville.
- Klein's four goals this season tied a career high.
- Nashville RW Patric Hornqvist returned after missing five games because of an undisclosed upper body injury.
- Predators D Roman Josi had two assists, the rookie's first NHL multipoint game.
- Thornton has 47 points in 35 games against Nashville.
- After Sunday, the Sharks will return to San Jose for a four-game homestand.