Despite the fast start by Edmonton, Chicago took over in stretches of the middle frame. Talbot was the difference with the goaltender stopping all 18 of their second-period shots.
The Oil rewarded their goalie's efforts and utilized another power play, late in the second, to increase their lead to three. At 19:52 of the period, Andrej Sekera shot the puck through traffic and it zipped past Crawford.
Sekera's goal was his second of the season, assisted by Ryan Nugent-Hopkins and Drake Caggiula. The 22-year-old rookie, Caggiula, now has a point in each of his first two NHL games.
Anton Slepyshev made it 4-0 at 7:17 of the third. The Oilers winger flung a shot on net and it slipped past the glove of Crawford. Jesse Puljujärvi was credited with the lone assist.
Draisaitl potted his second goal of the night from the slot, on the power play, at 18:35 of the third to cap off the Oilers five-goal performance. Jordan Eberle and Milan Lucic recorded the assists.
"(Chicago) is a team that's always in the playoffs," said Klefbom. "They're a really solid team all year so it was really good for this team and gives us a lot of confidence. I think we played a real solid home game here in Rogers Place so I am really happy with our performance."
The Oilers (11-8-1) hit the road to face the Colorado Avalanche on Wednesday night, followed by a date with the Coyotes in Arizona on Friday. The orange and blue are winners of two straight, outscoring their opponents 10-2 in the pair of victories.