Corey Perry put the Ducks in the lead in the second period, the Souray got the winner with just over two minute to play in regulation after Patrick Kane had equalised for Chicago.
The result means Anaheim close to within three points of Chicago at the top of the Western Conference.
Minnesota saw their seven game winning streak brought to an end as the Dallas Stars claimed a 5-3 victory over the Wild.
Jamie Benn, Ray Whitney and Cody Eakin had a goal and an assist apiece, while Erik Cole and Tomas Vincour also tallied.
The Tampa Bay Lightning beat the New Jersey Devils 5-4 via a shootout to give new coach Jon Cooper a win on debut, while the Columbus Blue Jackets were 6-4 winners over the Calgary Flames.