Artemi Panarin had a goal and two assists, Duncan Keith and Andrew Shaw also scored while Patrick Kane had two more assists to extend his point streak to 14 games, matching his career high.
After the Hawks let a 2-0 lead slip away, Shaw scored the go-ahead goal at 11:44 of the third period past Andres Nilsson. Leon Draisaitl sent the game to overtime with a goal with 2:46 left in regulation, but Hossa cashed in on his second breakaway chance of the game to start the Hawks' annual Circus Trip with two points.
But Hossa's 12th career overtime goal almost never happened.
Corey Crawford made a spectacular glove save on Taylor Hall to save the game minutes before. Crawford made 34 saves for his ninth win of the season. The win is his sixth straight against the Oilers, and the Hawks third straight.
Teuvo Teravainen sufferd an upper-body injury in the second period and did not return. Blackhawks coach Joel Quenneville told reporters it's "not serious" and lists him as "day-to-day." The 21-year-old registered just 5:33 of ice time before being forced from the contest. He has four goals and five assists in 18 games this season.
After a sleepy first period, Keith put the Hawks on the board at 7:26. Ketih went to the net and scored off a Kane feed on the man-advantage. Hossa looked to extend the lead to 2-0 on a breakaway moments later, but was denied. Panarin made up for it from close range via an Artem Anisimov pass through a traffic.
Jordan Eberle rifled a shot past Crawford on a breakaway two minutes later on a bad defensive change to cut the lead to 2-1 late in the second, and Benoit Pouliot erased the lead four minutes into the third.
The Hawks complete its swing through Alberta on Friday night against the Calgary Flames.