Logan Couture, Patrick Marleau and Marc-Edouard Vlasic also scored to help San Jose rebound from a lackluster effort Wednesday night against Winnipeg with Aaron Dell in goal that coach Peter DeBoer described as "lifeless."
The Sharks have won 10 of their past 12, continuing their turnaround after a 4-10-1 start. Jones was part of an improved defensive effort Friday, following the 5-1 loss to Winnipeg.
"We've got a lot of veteran guys in here," Jones said. "You go through it every year, tough stretches. It was pretty important to get it turned around as soon as you can and not let it spiral."
Jones was closing in on his 23rd career shutout until Kyle Clifford found the net with 1:49 left to finally get Los Angeles on the board.
The Sharks beat the Kings for the second time in five days. But unlike Monday, when San Jose blew a 3-0 lead before winning in overtime, the Sharks kept the pressure up in the rematch.
They came out fast and led 2-0 after one period despite being outshot 8-4.
Marcus Sorensen set up Marleau on the first score, faking a slap shot and directing a perfect pass to a waiting Marleau just to the right of the net. Vlasic's goal came on a delayed penalty, with the defenseman getting a screen from Couture and firing a slap shot from 50 feet out that found the net.
The Kings, who have played better recently despite bringing up the rear in the Pacific Division, couldn't climb out of their early hole.
"The big message was the first 10 minutes of the game was going to be huge, but we came out on the wrong side of that," defenseman Joakim Ryan said.
The Sharks increased their lead to 4-0 in the second period.
Just three minutes into the period, Gregor won a footrace to the puck down the left side and fired a wrist shot that beat Kings goalie Jonathan Quick to his glove side.
Gregor's first goal came in his 11th NHL game.
"You saw him really skating good after that," Sharks center Joe Thornton said. "It changes your mindset when you get that first one."
The Sharks welcomed center Tomas Hertl back to the lineup after he missed four games with a lower-body injury. Hertl resumed his place on the second line but left in the third period for what coach Peter DeBoer said was precautionary reasons.
Hertl is expected to travel with the Sharks for Saturday's game at Arizona.
Kings center Anze Kopitar had a four-game point streak snapped. He entered the day with 14 points (six goals, eight assists) over his previous 11 games. ... Marleau's first-period goal was the 557th of his career, moving him past Johnny Bucyk for 27th in NHL history. ... Sharks center Antti Suomela left the ice under his own power after taking a big hit from the Kings' Kurtis MacDermid in the third. Suomela's status was unknown after the game. ... The Sharks have scored the first goal in five consecutive games.
Kings: Host Winnipeg on Saturday night.
Sharks: At Arizona on Saturday night.
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