Stoll's shootout goal overcame a late tying score from San Jose's Joe Thornton, as the Oilers made their first step towards erasing the memory of last season's late collapse with a 3-2 victory over the Sharks on Thursday night.
The Oilers, who finished with just two wins in their last 20 games last season, bounced back in the opener.
"It's good to battle and get the two points and to find a way to win the game," Stoll said. "We had the game there and with 11 seconds we lose it. But that's what good teams do, they find a way to win even when you have some adversity."
Patrick Marleau scored San Jose's other goal.
The Oilers have undergone a youth movement with the likes of Gilbert, Brodziak, Sam Gagner, Robert Nilsson and Andrew Cogliano and coach Craig MacTavish was impressed by the young players.
"It's a great story when you have a lot of young guys here and helping," MacTavish said. "Now we just have see how substantive it is. Those guys made plays and it was good to see that they didn't get caught defensively."
Thornton said the Sharks were happy just to come back and earn a point.
"We had a pretty good first, a terrible second and an average third," he said. "We have lots of room to improve. It's a tough place to play and to get a point out of their home opener is something we're going to have to be happy with."
The game was scoreless until Marleau got the Sharks on the board off a pass from Thornton 26 seconds into the third period.
Edmonton was quick to respond just over a minute later as a trio of rookies connected. Sam Gagner and Andrew Cogliano earned their first NHL points when Cogliano snapped a shot that deflected off the skate of Gilbert in front of the Sharks' net and in.
The Oilers took the lead just over a minute later as Sheldon Souray sent a shot from the point that got behind Sharks goalie Evgeni Nabokov. Brodziak, another Oilers newcomer, dove to sweep the puck in to put Edmonton ahead 2-1.
But with Souray in the box and Nabokov on the bench, the Sharks were able to send it to overtime when Thornton blasted one past Dwayne Roloson with time running down.
Roloson finished with 28 saves and Nabokov had 23.
San Jose had the best chance in the scoreless first period, as Torrey Mitchell rang one off the post 13 minutes in and the rebound landed on the goal-line before Roloson swept the puck away.
The zeros stayed up on the scoreboard through the second as well with the teams only able to muster four shots apiece.
New captain Ethan Moreau was not in the Oilers' lineup. Moreau is still recovering from a bone bruise after taking a shot on the foot in the preseason. Geoff Sanderson took his place. ... Sharks rookie Devin Setoguchi, forced to leave San Jose's practice on Thursday due to a foot injury after taking a puck in the preseason, also missed the game. ... Veteran forward Jeremy Roenick made his Sharks debut. ... Before the game, the Oilers observed a moment of silence to honor the memory of local hockey star Billy Warwick, who died Wednesday at 83. A member of the Penticton Vees that won the world championship in 1955, Warwick led the Canadians in scoring with 14 goals and seven assists.