Dostal became the third rookie goalie in franchise history to record a shutout, joining John Gibson (six) and Ilya Bryzgalov (one).
Frank Vatrano got his 30th goal of the season at 10:31 of the third period when the Ducks had a two-man advantage. He is the second undrafted player in franchise history to reach the 30-goal mark — joining Andy McDonald, who scored 34 in 2005-06.
Brett Leason had a goal and an assist for the Ducks, who had been outscored 35-7 during their skid.
Arvid Soderblom made 21 saves for Chicago, which has dropped three of its last four.
Ducks rookie Leo Carlsson, the second overall pick in the 2022 NHL draft, did not return after being involved in a knee-on-knee collision with Chicago defenseman Alex Vlasic during the second period. Carlsson has already missed 20 games due to an MCL sprain and concussion.
Killorn got the Ducks on the board at 3:10 of the second period when he tipped in Gustav Lindstrom’s shot.
After Leason’s wrist shot beat Soderblom at 9:34, Killorn buried a snap shot from the left faceoff circle with 1:34 remaining to make it 3-0.
Vatrano’s power play goal marked the first time in six games the Ducks had scored with the man advantage.
Up next for the Ducks: vs. Tampa Bay at Honda Center on Sunday.