Edmonton ran off a season-high four straight wins from Nov. 13-20 but has gone just 1-6-1 since, including Tuesday's 3-2 home loss to Carolina.
Tommy Salo returned to the net for the Oilers after sitting out more than a month because of a hip injury. He surrendered two first-period goals to Marty Murray before settling down to make 22 saves in his first appearance since Nov. 8.
"It doesn't matter how you give up the goals, you're still disappointed," Salo said. "It's tough when you're down 2-0 in the first period and you have to catch them."
The Oilers' NHL-worst power play went 1-for-6 as Edmonton failed to score more than two goals for the fifth time in six games.
"Sixty minutes is what we need to be successful," Oilers forward Ryan Smyth said. "We didn't initiate as far as coming out banging. That cost us some momentum."
The Sharks ended November on a seven-game unbeaten streak (5-0-2), including a season-high five-game winning streak, but have gone just 1-2-1 in December.
On Wednesday, San Jose carried a two-goal lead into the second period but then fell apart, suffering a 3-2 loss to the Anaheim Mighty Ducks.
Vesa Toskala, filling in for injured starter Evgeni Nabokov, made 27 saves for San Jose, which squandered a chance to move within one point of first-place Los Angeles in the tightly packed Pacific Division.