Dwight King and Jeff Carter also had a goal and an assist apiece for the Kings, who ran over their California rivals for their eighth win in nine games to cap a 15-2-4 stretch since Nov. 2.
Jones' shutout streak ended at 133 minutes, 26 seconds, but Patrick Marleau's goal with 2:10 to play was just the sixth Jones has allowed in his club-record 7-0 start.
Kings captain Dustin Brown was ejected for a knee-on-knee hit on Tomas Hertl late in the first period. San Jose's rookie goal-scorer didn't return to the game.
Jones has been spectacular since his NHL debut on Dec. 3, keeping the Kings on a roll without injured starter Jonathan Quick. Jones didn't give up a goal in his first eight periods at Staples Center, shutting out the New York Islanders and Edmonton before Marleau's late goal.
Already the first goalie since the 1938-39 NHL season to record three shutouts in his first six starts, Jones is one victory shy of Bob Froese's NHL record 8-0 start. Jones even earned an assist in the second period on a goal by Toffoli.
Antti Niemi stopped 28 shots on a miserable night for the Sharks, who have lost six of eight while falling off the pace set by their two Southern California rivals, who have two of the NHL's four best records.
The home team has won 15 straight games between San Jose and Los Angeles, including all seven in the Kings' second-round playoff series victory last spring.
Brown and Hertl collided late in the scoreless first period, with Brown making a cut at the Sharks' blue line before their right knees connected. Hertl dropped his equipment and limped to the bench while Brown was tossed, but Los Angeles killed the ensuing power play.
Shortly after Alec Martinez opened the scoring with a wobbly slap shot off Toffoli's pass, Toffoli added his ninth goal in impressive fashion, getting an extra-long pass from Slava Voynov and beating Niemi with a vicious wrist shot.
The Sharks had two golden opportunities to score on the same sequence late in the period, but Joe Pavelski whiffed on an open net before Tommy Wingels botched an ensuing wraparound chance, allowing a facedown Jones to clear the puck off the goal line with his glove while facing the other way.
In the opening minute of the third, Carter tapped in his 10th goal off a pass from King, who bulled past San Jose's Justin Braun after the Sharks' neutral-zone turnover. King then chopped home a rebound while Carter generated traffic in front of Niemi.
NOTES: Kings D Willie Mitchell missed his third straight game with an injury. ... D Scott Hannan returned to San Jose's lineup after missing five games with an upper-body injury. The Sharks scratched Jason Demers. ... The Kings have allowed a first-period goal once in 21 games. ... Marleau played in his 1,200th career game, and Los Angeles D Drew Doughty played in his 400th. Both have spent their entire careers with one team after making an NHL roster as 18-year-old prodigies.