He helped them pick up two Wednesday night.
After Couture pulled the Sharks within a goal on a power play at 6:50 of the third, Tommy Wingels tied it at 9:15. San Jose snapped a two-game losing streak with its second victory in eight games.
"It's a battle every night," Couture said. "There are no easy points in this conference; every single team is so good. To win the way that we were able to and come back with two goals in the third, hopefully that can get us going in the right direction.
"We needed something. We need all the points we can get right now," he said. "We need to find ways to get points every single night right now."
Sharks coach Todd McLellan credited Couture for being a real spark for the team in the comeback win.
"Logan is always really determined, but he gets excited to come here and play in Edmonton; I don't know why," he said. "He had six shots on goal, a couple of goals and an amazing shot in the shootout. We're really proud of him and we're happy to have him."
The Oilers opened the scoring midway through the first period on a power play. Nail Yakupov fed the puck across the ice to Gagner, who had time to tee up a slap shot from the top of the circle that beat Antti Niemi to the glove side. It was Gagner's 12th goal of the season.
"It is very disappointing losing the penalty shots," Oilers coach Ralph Krueger said. "We are a good team at that.
"It's painful, but we have to look at the fact that we have points in five games and move forward," he said. "But right now of course the pain of giving up a 3-1 lead dominates."
Couture tied it off a rebound with just less than six minutes to play in the period.
Edmonton regained the lead with 8 minutes left in the second period. Nick Schultz picked up a pass as he stepped on the ice from the penalty box, raced in on a 2-on-1 and fed Horcoff.
The Oilers made it 3-1 early in the third period when Jones stole the puck from defender Matt Irwin behind the San Jose net and hooked around to send the puck through Niemi's legs.
Couture scored his 14th goal of the season to make it 3-2, sending a shot through traffic and past Dubnyk, and Wingels tied it with a quick wrist shot.
Both teams are off until Saturday. Edmonton closes out a four-game homestand against St. Louis, and the Sharks are at Minnesota for the fourth game of a five-game trip. ... It was the last of three meetings between the two teams. The Sharks spoiled the Oilers' home opener Jan. 22 by scoring six first-period goals in a 6-3 win, and San Jose won 3-2 at home in a shootout. ... Edmonton's Ryan Nugent-Hopkins missed the game because of the flu. ... Defenseman Marc-Edouard Vlasic played in his 500th NHL game, all with San Jose.