Gustav Nyquist scored twice one day after he scored his first of the season. Andreas Athanasiou scored a third-period goal, his first of the season.
Detroit played strong defense in the first period, holding San Jose to six shots despite having to kill two power plays. Jones made 11 of his 29 saves for the Sharks (3-3-0).
"The start was OK, but we needed to finish one of those early chances," San Jose forward Joe Pavelski said. "We let them hang around in the first period, and everything got away from us after that."
The Red Wings killed another penalty early in the second, then took a 1-0 lead at 4:14 when Nyquist finished a 2-on-1 with a wrist shot over Jones' left shoulder.
Nyquist made it 2-0 at 15:10 of the second period. Ryan Sproul forced a turnover in the Sharks zone and Nyquist beat Jones with a wrist shot under his left arm.
"We talked about their transition game before the game, and then we played right into their hands," Sharks coach Peter DeBoer said. "We were late to everything, and when you are a step behind against that team, they will take advantage."
The Sharks almost scored at the end of the second period, but Logan Couture and Brent Burns each hit the post in the final three seconds.
Athanasiou gave the Red Wings a 3-0 lead at 6:05 of the third period, taking a cross-ice pass from Thomas Vanek with an open path to the net. He took a slap shot from the top of the left faceoff circle and beat Jones on the glove side.