After a goalless first period in which Anaheim was outshot 13-7, the Ducks scored three times in the second to take a 3-0 lead.
Killorn gave Anaheim a 1-0 lead at 3:10 when he tipped in a shot from defenseman Gustav Lindstrom.
"As the game went on, I thought we got more confident, and then we got that first goal," Ducks coach Greg Cronin said. "You could feel a lot of weight lifted off the bench."
Leason made it 2-0 at 9:34 with a wrist shot from the top of the right face-off circle after entering the Chicago zone with speed.
"A lot of passes were either hitting our tape and going off, or they weren't flat, or we weren't supporting each other," Chicago defenseman Jaycob Megna said. "We just seemed too spread out and just not connected enough."
Killorn extended the lead to 3-0 at 18:26 with his second of the game, on a wrist shot from the right circle.
Killorn has seven goals in the past 12 games after scoring seven in his first 39.
"Typically, over a season, it kind of evens itself out," Killorn said. "I just want to continue to do that for the rest of the season."
Frank Vatrano scored his 30th goal of the season during a 5-on-3 power play at 10:31 of the third period for the 4-0 final. It was his first goal in 10 games.
"He's been sitting on 29 for a little bit, so just nice for him to get that and not have to worry about that anymore," Killorn said.