Karlsson had three assists and has 25 points (one goal, 24 assists) in his past 14 games for the Sharks (25-13-7).
Karlsson joined Paul Coffey (17 games, Nov. 27, 1985-Jan. 2, 1986), Brian Leetch (15 games, Nov. 29-Dec. 31, 1991), Bobby Orr (14 games, Dec. 13, 1970-Jan. 14, 1971) and Phil Housley (14 games, Dec. 26, 1992-Jan. 19, 1993) in that group.
"He's been great," Sharks forward Joe Pavelski said. "He's really established his game in our structure. Everybody feels pretty comfortable playing with him because he makes those plays and he makes the outlet pass and he's got that speed coming out of our end with it. He's been a big piece to our success lately."
WATCH: [All Oilers vs. Sharks highlights]
Evander Kane and Joonas Donskoi each scored two goals, and Brent Burns had a goal and an assist. Marcus Sorensen and Joe Thornton also scored, and Aaron Dell made 20 saves for the Sharks.
Alex Chiasson and Milan Lucic scored for Edmonton (20-20-3). Cam Talbot gave up four goals on 17 shots and was replaced by Mikko Koskinen at 7:54 of the second period. Koskinen made 16 saves.
The Sharks defeated the Oilers for a second straight time. They also won 7-4 on Dec. 29 at Rogers Place.
"They were attacking us," Edmonton coach Ken Hitchcock said. "That's two games in a row they've owned us in front of the net, in the slot, and they knocked us out of the box. That's a damn good team. They owned us in what I call critical ice; the areas you score in.
"We had our chances and they got sticks on the puck or got deflections. They played better than we did in those critical zones."