The Blackhawks overcame a 2-0 deficit to remain unbeaten and became the first team in the NHL this year with four victories.
Hossa's winning goal came with Brenden Morrow in the penalty box. The Dallas captain was called for interference just 22 seconds into the overtime period.
Loui Eriksson gave Dallas the lead when he scored shorthanded with only a second left in the first period.
All three Chicago goals came on the power play.
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