The Ducks ended a four-game losing streak and handed the Blackhawks only their fifth non-overtime setback of the season.
The winning goal came when Souray fired a slap shot that tipped off the stick of a Chicago defender past Ray Emery.
Emery had played in 16 games this season and this was his first loss of the year. He stopped 22 shots.
Jonas Hiller made 25 saves for the Ducks, who despite the recent losing streak still have the second-best record in the Western Conference and are within three points of the Blackhawks for the top spot.