"It's always good to get that first one out of the way," Tennyson said of his first NHL goal. "It tied it up for us and that makes it even better. I was trying to go off the far post and I don't know if it was tipped or misplayed. I'll take it."
"It got better as it went on," Sharks Joe Pavelski said. "It took us a little longer than we wanted to get going."
Steven Pinizzotto and Ryan Nugent-Hopkins scored a couple of minutes apart in the second period to give the offensively challenged Oilers a 3-2 lead. Boyd Gordon, in his first game since returning from a back injury, also scored.
Edmonton scored three goals for the first time in 10 games but still fell a fifth straight time in San Jose. The Oliers have not won when scoring at least three goals since Nov. 9, a span of 19 games. Edmonton has scored a league low 69 goals.
"Close isn't good enough," Gordon said. "We're struggling to win games the whole season and tonight was a prime example of that."
Antti Niemi saved 25 of 28 shots for the Sharks to remain undefeated (5-0-1) against the Oilers in San Jose.
Scrivens stopped 26 of 30 shots as Oilers interim coach Todd Nelson saw his bid for a victory in his second game at the helm fall short.
Gordon gave the Oilers, who are 1-12-5 since Nov. 11, the early lead with his fifth goal of the season late in the first period. David Perron's pass found Gordon open in front of the net.
"I like the effort," Gordon said. "It's just a mistake here and there and that's a really good hockey team and they make you pay."
Sheppard tied the game early in the second period with his fourth goal, and the first since scoring in three straight between Nov. 1-8 -- a span of 18 games.
Couture scored less than two minutes later to put the Sharks on top, but Pinizzotto tied the game when he batted the puck into the net during a scramble in front of Niemi.
Nugent-Hopkins scored on a rebound from a shot by Jordan Eberle, who has 10 points in his last seven games against the Sharks.
Tennyson scored his first NHL goal during a power play and Goodrow followed with the game winner shortly thereafter.
"I had a sense a guy would catch me and I tried to fight him off the best I could," Goodrow said. "I was yelling but I don't know if (Brent) Burnsie heard me. He made a great pass up the middle."
NOTES: Perron had his first multiple point game since the season's second game on Oct. 11. . Oilers F Matt Hendricks assisted on Pinizzotto's goal to end a nine-game scoreless streak. . The Oilers only win over their past 18 games is against the Sharks. . Couture has 12 points in his last 11 games. . Oilers F Taylor Hall extended his career-long scoreless streak to 11 games. . The Sharks and Oilers were playing each other for the third time in 12 days.