Logan Thompson made 32 saves for the Golden Knights (41-30-5), who have lost three of five (2-2-1).
Vegas is three points behind the Kings for third place in the Pacific and four points behind the Dallas Stars and Nashville Predators for the wild cards from the Western Conference.
''We have to regroup,'' Vegas coach Peter DeBoer said. ''We've talked about this, we knew we weren't going to run the table and we talked about two weeks ago, we were going to drop some points along the way, but we're still right in the thick of things. We have to have a short memory and get ready for the next one (against the New Jersey Devils on Monday).''
Russell gave Edmonton a 1-0 lead at 16:26 of the first period. Zack Kassian passed up a shooting opportunity at the side of the net with Thompson down and decided to slide the puck back to Russell in the high slot.
It was Russell's first goal in 126 games; he hadn't scored since Mar. 17, 2019, also against the Golden Knights.
"I didn't know that; actually, we have been having a few dinners on the road," Kassian said. "I didn't want the freebie. Looking at the replay, it rolled on me for a second there and I could have probably flicked it over the goalie, but then I saw 'Rusty' coming down, so I figured I'd give him a shot. He bought me a few meals on the road, so I thought I would give him a freebie."
Cody Ceci scored 35 seconds into the third period on a point shot through traffic to make it 2-0, and Warren Foegele made it 3-0 on a breakaway at 5:16 after a turnover by Alec Martinez at the Oilers blue line.