Making his third consecutive start, Hutton stopped eight in the first, 10 in the second, and 18 in the third.
"They are a pretty solid team, and they are going to get their chances," Hutton said. "We kind of bent, but we didn't break. We weathered the storm and held on for a big two points."
Earlier this week, Hutton backstopped the Predators to wins Tuesday in New York against the Rangers and Thursday at home against Dallas. He ended the week with a 3-0-0 record, stopping 97 of the 101 shots he faced.
Nystrom scored the game's first goal at 16:04 of the opening period.
From above the left faceoff circle, Predators defenseman Victor Bartley sent a wrist shot toward the San Jose goal. The puck deflected off Nystrom's leg, then his stick and into the net for his sixth goal of the season.
Nystrom is just one goal off the Nashville team lead.
Entering Saturday, San Jose had outscored opponents 42-14 in the first period this season.
Nashville is 12-0-1 when leading after one period this season.
Josi doubled the Nashville lead at 18:08 of the second.
With the Predators on a power play, Craig Smith had the puck below the San Jose goal line. He found Josi all alone at the center of the blue line, and the Swiss defenseman skated into the slot and beat Sharks goaltender Antti Niemi with a wrist shot high to the glove side.
"We had a great battle in the corner, I think there four of their guys against our three guys, and we won the puck," Josi said. "That was huge and (Smith) made a great play to me."
The Sharks had not allowed a power-play goal in their previous four games.
"Every game we play it seems the team that wins the special teams play, wins the game," San Jose captain Joe Thornton said. "Tonight they got the one power-play goal and we didn't, and that's basically what the NHL comes down to right now, who is better on special teams."
San Jose got on the board at 7:28 of the third when Boyle redirected Matt Irwin's shot from the high slot past Hutton for his sixth of the season.
"We weren't nearly aggressive enough," San Jose coach Todd McLellan said. "It's amazing, in the third when we played on the inside a little bit more, we got more second chances, kept the forecheck alive, we were a much different team. I'm a bit disappointed in the first period and a half to two periods."
Nashville regained its two-goal lead at 17:21 of the third when Stalberg carried the puck down the left side and beat Niemi with a wrist shot from above the left faceoff dot.
"That was huge," Nashville coach Barry Trotz said. "That ended up being a real important goal, the game-winning goal."
Marleau drew the Sharks within one with 54.6 seconds remaining in the third when he tipped home a nice pass from Boyle.
Josi has points in four consecutive games. ... Smith returned to the Nashville lineup after missing the past three with flu-like symptoms. ... Boyle leads Sharks defensemen with 17 points this season.
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NASHVILLE, TN - DECEMBER 14: Marek Mazanec #39 of the Nashville Predators works to cover the net without his stick...