Jones followed up a 41-save performance in a 2-1 win Monday with another sharp effort to become the first Sharks goalie with at least 40 saves in consecutive games since Arturs Irbe in 1993, according to SportRadar.
After getting pulled five times in his first 15 starts this year, Jones has allowed just five goals on 147 shots in his past four.
"This is probably the best I've seen him play in a long, long time," coach Bob Boughner said. "He looks confident and he looks like he's reading the play better."
Evander Kane scored twice, and Rudolfs Balcers and Tomas Hertl also scored to give the Sharks a sweep of the two-game series.
Alex Iafallo and Adrian Kempe scored for the Kings, and Cal Petersen made 24 saves. Los Angeles has lost five of seven.
"It's disappointing for sure," defenseman Drew Doughty said. "San Jose is a good team. I believe we can win every game. But this was a series, before we started, I really believed we could win and outplay them. We did at times but we just didn't get the job done."
The Sharks opened the scoring by converting on two well-executed rushes in the second period. Balcers scored his third of the season on a give-and-go with Marcus Sorensen to make it 1-0 early in the period.
Kane added to the lead late in the second when he sent a cross-ice feed to Kevin Labanc after entering the offensive zone. Labanc left the puck on a short pass for Brent Burns, who found Kane down low for his 13th goal.
"That was as poor rush coverage as I've seen from our group of D, and our forwards set up rushes by poor game management," Kings coach Todd McLellan said. "We got impatient and they stung us for it."
The Kings responded with 12.4 seconds left in the period when Iafallo finally got one past Jones after being robbed multiple times the past two games. Iafallo redirected Dustin Brown's pass from the point to make it 2-1.
The Sharks broke the game open in the first two minutes of the third, with Kane getting his second goal on a deflection of Mario Ferraro's point shot and Hertl beating Petersen on the rush.
"We came out and attacked," Boughner said. "We took the momentum back that we gave them at the end of the second period. I was happy to see that."
Kempe got one of those goals back for the Kings, but Los Angeles couldn't get any closer.
Sharks captain Logan Couture left late in the third period after being hit hard near center ice by Los Angeles' Jeff Carter. Couture stayed down for a couple of minutes before skating off under his own power and going straight to the dressing room. Carter was called for high-sticking on the play.
"It looked a little high to me," Boughner said. "Looked like it could have been the butt end come up. ... Let the league look at it and let them see what they think."
Sharks forward Kurtis Gabriel was benched after he got fined by the NHL for cross-checking Kings defenseman Kurtis MacDermid during pregame warmups Monday. The two former minor league teammates fought in the first period that night and Gabriel was fined about $3,000 by the NHL on Tuesday. Boughner, also fined $5,000, decided to sit Gabriel.
Kings: Visit the Vegas Golden Knights on Monday night.
Sharks: At the Arizona Coyotes on Friday night.
Kane nets 2 goals in Sharks' win vs. Kings
Evander Kane score a goal in the second period and another in the third as the Sharks go on to defeat the Kings 4-2 at home.