Hossa collected the rebound and fired a shot that Khabibulin also turned aside but then put the second rebound past him for the game-winner 1:44 into the extra frame.
Viktor Stalberg and Patrick Kane also scored for Chicago, which notched its 19th game without a regulation loss to begin the season, improving to 16-0-3 overall.
Ray Emery made 17 saves for the Blackhawks.
Khabibulin finished with 31 stops for the Oilers, who fell for the third time in four games.
Jeff Petry and Nail Yakupov scored for Edmonton.