In enemy territory, San Jose outshot Edmonton 18-3 in the third period, and 6-2 in the short overtime.
"We took an honest evaluation of that first period and we did a lot of good things," Sharks coach Peter DeBoer said. "They happened to score with two of their first three chances.
"At the end of the first the message from me, and more importantly, from the guys in the room, was that we feel good about our game, let's just stick with it."
San Jose, which has played 110 playoff games since the Oilers were last in the postseason in 2006, got steady performances throughout its lineup Wednesday.
"You guys keep talking about experience," DeBoer said. "I thought some of our best players were young guys tonight. (Marcus) Sorensen, (Timo) Meier, (Chris) Tierney were fantastic.
"We have a group of men in there that play the right way and have a history of knowing how to play at this time of year, playing selfless and working for each other. So I might be the only one here who's not surprised by how we played tonight."
The Oilers weren't blaming their relative lack of playoff experience for the big shift in momentum.
"I liked our start. We were edgy and playing on our toes, and then we started taking some penalties, especially in the O-zone," Oilers coach Todd McLellan said. "We took four O-zone penalties in a row and they're a savvy team, they're a veteran team, they took advantage of it, scored a goal and they established their momentum allowing them to get back in the game.
"They were able to grab the game and we were unable to grab it back."