Mathieu Roy added his first career goal as Edmonton took a 3-0 lead in the first 11½ minutes. Dwayne Roloson made 32 saves as the Oilers held on in their first trip to the Shark Tank since last season's Western Conference semifinals, won in six games by Edmonton after San Jose took a two-game lead into overtime of Game 3.
Ales Hemsky extended his scoring streak to six games with an assist on Bergeron's goal.
Jonathan Cheechoo scored the Sharks' 14th power play goal in four games, but their three-game winning streak was snapped when they couldn't rally from the early deficit. Marcel Goc also scored, and Evgeni Nabokov made 13 saves in his fourth straight winless start
The Oilers have earned a point from five straight games after a four-game losing streak.
The Sharks' penchant for slow starts at home doomed them again. San Jose's opponents have scored the opening goal in eight of its nine home games since Dec. 11, with the Sharks' win over Columbus on Saturday as the only exception.
Bergeron scored a power-play goal just 95 seconds in, with his long slap shot eluding Nabokov. Roy, who was named to the American Hockey League all-star game this week, got his first goal in five NHL games from a similar spot, and Stoll added his 13th of the season just 36 seconds later.
The Sharks had bombarded Dallas, Detroit and Columbus for 13 power-play goals in their previous three games, but didn't get much of a chance to use their vaunted man-advantage attack. The officials kept San Jose on a parade to the penalty box with seven straight minor penalties in the first two periods.
Edmonton didn't receive a minor until Matt Greene was called for interference with 2:15 left in the second period, drawing a sarcastic standing ovation from the Shark Tank crowd.
The San Jose power play finally broke through on a hard shot by Cheechoo early in the third period. Cheechoo, voted an all-star game starter despite having just 14 goals and a minus-10 rating, has heated up lately with three goals in his last four games.
Edmonton's penalty-killing unit was the NHL's fourth-best entering the night, and the Oilers did an outstanding job disrupting San Jose's side-to-side puck movement. San Jose jumped into the NHL lead in power-play goals with its recent scoring spree.
Notes: Sharks C Joe Thornton didn't score after racking up 10 points in the last three games.