WATCH: [All Sharks vs. Devils highlights]
It was Jones' 16th NHL shutout, his first since a 4-0 win on 26 saves against New Jersey on Nov. 21.
"The Devils came out pretty hard; they're good around the net with quick plays, but I thought we were really good," Jones said. "Our penalty kill was very good again and that was probably the difference."
The Devils, who were tied for seventh in the NHL on the power play, went 0-for-5.
Melker Karlsson, Joe Pavelski and Joonas Donskoi scored, and Justin Braun had two assists for the Sharks (3-3-0), who have won three of their past four games.
Keith Kinkaid made 30 saves for the Devils (6-2-0), who had a three-game winning streak end.
"I don't want to say they slowed us down, but they did a good job of creating turnovers," New Jersey defenseman Andy Greene said. "That falls on us a little bit. The way they play in the neutral zone forces you to do a lot of chips and having our weak side guy slash across and use our speed. We were a little stubborn and didn't do that as well and it fed right into their game."
San Jose scored twice in the second period to take a 3-0 lead. Pavelski scored his second goal of the season at 5:49 before Donskoi scored his first on a backhand at 18:50.
Karlsson scored his first of the season into the top right corner past Kinkaid 14:11 into the first period. Tomas Hertl made the play possible when he fought off a check from defenseman John Moore before finding Karlsson at the left post.