Hossa scored the first and last goals for Chicago as they inflicted the first loss on Anaheim in nine games and just the second in 20 on Friday.
In a frenetic final period, the Blackhawks took a 3-0 lead with less than 10 minutes left only for the Ducks to strike twice in a minute to stay in the contest.
But the home side held on at Chicago's United Center and Hossa ensured victory in the dying seconds with a goal into Anaheim's empty net as the visitors chased an equaliser.
Despite the loss, the Ducks (36-9) still have the best win-loss record in the NHL and remain top of the Western Conference's Pacific division with 77 points.
Cam Fowler of the Anaheim Ducks tries to take down Marian Hossa of the Chicago Blackhawks. Photo by Jonathan Daniel/Getty Images
The Blackhawks moved up to 73 points with their victory, extending their margin at the top of the West's Central standings to four.
Chicago led 2-0 at the end of the first period against Anaheim thanks to goals from Hossa and Kris Versteeg and after a scoreless second stanza, the hosts looked in control when Bryan Bickell struck with 10:13 gone in the third.
Goals from Ryan Getzlaf and Kyle Palmieri for the Ducks followed soon after but the visitors could not manage a third goal and by the time Hossa scored with eight seconds left, the game was effectively already over.
Jonas Hiller of the Anaheim Ducks ends up on his back in the net after Bryan Bickellof the Chicago Blackhawks scored a goal. Photo by Jonathan Daniel/Getty Images
The Columbus Blue Jackets notched their fifth win in succession, crushing the Washington Capitals 5-1.
Cam Atkinson scored twice for the Blue Jackets, who moved to within three points of the second-placed Philadelphia Flyers in the Eastern Conference's Metropolitan division, while Washington (52 points) sit fourth.