Dwight King and Jordan Nolan scored during another dominant night for Jones, who became the first goalie in Kings history to begin his career with six consecutive victories. Edmonton couldn't solve Jones, who has allowed just five goals in his six games.
Ilya Bryzgalov stopped 37 shots for the last-place Oilers, who have lost four straight.
Dustin Brown added an empty-net goal for the Kings, who have won seven of eight while taking just two regulation losses in 20 games since Nov. 2 (14-2-4).
Jones made a handful of stunning saves in another defence-dominated night for the Kings, whose 68 goals allowed are the fewest in the NHL.
Bryzgalov almost matched the Kings' youngster as Los Angeles handily outshot the Oilers.
The Kings had to go right back to work after sweeping through eastern Canada on a four-game road trip last week, posting convincing victories on every stop of their showcase in Montreal, Toronto and Ottawa. Los Angeles lost Sunday in Chicago before returning to Staples Center for its third game in four nights.
But the Kings got the first period's only goal when Drew Doughty stickhandled through the Edmonton end before finding King for his ninth goal. King has two goals in his last three games after a 10-game drought.
The Kings did nothing with two power plays during the scoreless second period, but Jones denied Ryan Smyth and Nail Yakupov up close on unguarded chances. Jones then stopped Taylor Hall on a clean breakaway early in the third, and Edmonton didn't register its first shot on goal until midway through the period.
Matt Greene then made an exceptional play from in front of the Oilers' bench, capitalizing on a bad Edmonton change to lob a pass to Nolan for a breakaway goal, his fifth of the season.
Edmonton pulled Bryzgalov after Brown took a penalty in the waning minutes, but the Kings weathered the 6-on-4 disadvantage before Brown emerged from the box at exactly the right time to skate in alone for his empty-netter, the 400th point of his career.
High-scoring right wing Ales Hemsky returned to Edmonton's lineup after missing Sunday's loss in Anaheim with sore ribs.
NOTES: Edmonton D Corey Potter served the first half of his two-game suspension for boarding Anaheim's Nick Bonino from behind on Sunday. Anton Belov returned to the Oilers' lineup in his place. ... Kings D Willie Mitchell missed his second straight game after getting hit by Chris Neil in Ottawa. Mitchell's absence has coincided with Greene's return from a 15-game injury absence. ... Los Angeles also made two switches on its forward lines, activating Linden Vey and Matt Frattin while scratching Daniel Carcillo and Kyle Clifford.