The 20 year-old rookie tipped Robert Nilsson's cross-ice pass three minutes into overtime for his 15th goal of the season. He had given the Oilers a 5-4 lead early in the 3rd period.
The Hawks picked up a point to move within five points of the final playoff spot in the Western Conference while the Oilers improved their overtime/shootout record to 17-5 and are just two points behind the Hawks.
Chicago's Dustin Byflugien tied the game at 15:25 of the 3rd period with his 16th goal when he knocked down his own rebound shot and banged the puck past goalie Mathieu Garon just outside the crease.
Cogliano almost won the game in regulation at the 18 minute mark, but Hawks goalie Patrick Lalime blocked his stuff-in attempt.
Edmonton took the lead on a power play three minutes into the game when Dustin Penner tallied his 19th on a quick turnaround shot from 5-feet out.
Less than five minutes later, Patrick Sharp tied the match with his team-leading and career high 34th goal by firing a 25-footer over Garon's glove after taking a pass from Jonathan Toews and Patrick Kane.
Late in the period and stretching into the 2nd period, the Hawks had a two-man advantage for 99 seconds and peppered Garon with several shots, but couldn't score.
Defenseman Duncan Keith gave Chicago the 2-1 lead at 8:22 with his career high 10th goal by blasting a 25-footer past Garon on the short side. However, the Oilers tied it again less then two minutes later when Curtis Glencross beat Lalime with a 10-footer over his shoulder.
The Hawks regained the lead at 11:53 when Jason Williams knocked in Andrew Ladd's rebound while on his knees at the edge of the crease for his 11th goal.
Just before the period ended at 18:36, the Oilers knotted the score at 3-3 when the puck bounced off a Hawk skate and Nilsson slipped a short shot past Lalime.
At the start of the 3rd period, Edmonton regained the lead off a faceoff, again bouncing off a Hawk player, and Marty Reasoner whirled around on a backhander for his 8th goal.
Two minutes later at 3:17 on a power play, the Hawks tied things up at 4-4 when Robert Lang fired in his 19th goal on a 27-footer with Ladd providing a screen.
Cogliano put the visitors up 5-4 at 6:12 and Byfuglien tied it again at 15:25 to send things into overtime.
The Hawks outshot the Oilers 38-25, especially dominating in the 2nd period 17-3.
Byfuglien and Williams led all shooters with six shots each with the Hawks 1-of-6 on the power play; the Oilers were 1-of-3.
Forward Kevyn Adams returned to action after missing 54 games following knee surgery.
The Hawks will head to Detroit Tuesday to face the conference leading Red Wings and then return to the United Center Wednesday to take on Carolina (7:30 pm).
AP Notes: Chicago C Kevyn Adams returned after missing 54 games following knee surgery. ... Including Khabibulin, five Chicago regulars sat out with injuries: LW Martin Havlat, D Brent Sopel, C Yanic Perreault and LW Ben Eager. ... Edmonton D Ladislav Smid returned after missing seven games with a right knee and ankle sprain. ... Oilers LW Geoff Sanderson missed his second game with a low back sprain. ... Still on injured reserve for Edmonton are C Shawn Horcoff, LW Raffi Torres, LW Ethan Moreau (out for the season) and D Sheldon Souray.
Head coach Craig MacTavish: "It was a good, gratifying win to come in here and win both games on this road trip; good energy-building win for us. They played great. Marty [Reasoner] had great chances, too, tonight. He had months worth of chances in one game. The kid line was exceptional start to finish. I think both teams have a real good, bright future with the amount of good young players both of us have in our lineup and I think that creates a little competitiveness between the young players on both teams to outplay the other guys. It's almost like they seize the opportunity to go against Chicago's really good young players, too, as well. It had to help competitively. Players like that, they rise to the occasion. Both teams have a number of really good players but our guys were just a little bit better tonight."
Center Andrew Cogliano: "A lot of penalties that went our way ... our penalty kill, with the vets, they're doing an unbelievable job on the PK when we have trouble like that. As of right now we have pretty much all lines scoring. I think Sam played pretty unbelievable tonight, two unbelievable passes by him. [Jonathan] Toews and [Patrick] Kane played pretty good. They're obviously one of their go-to guys."
Center Sam Gagner: "We know how big every goal is right now, in every game and we approach every shift with that intensity. That's why we've been successful the last little while here and hopefully we keep it going.
"They [Jonathan Toews and Patrick Kane] both had pretty strong games. They're both good players in this league at such a young age, which is tough to do. We're just trying to go out there and make plays. I don't think we really approach the battle of the young guns so much as a battle for our playoff spot here. A lot of guys stepped up, there were some big shot blocks when we needed it and some big saves by Mattie [Garon]. It was a big win for us."