Ryan Nugent-Hopkins made it 3-0 at 15:58. He came onto the ice for Ryan McLeod, immediately received a pass from Barrie and scored on a wrist shot from the top of the right circle.
Jesse Puljujarvi scored at 4:15 of the second period to stretch the lead to 4-0.
"We talked about playing a full 60 (minutes) tonight, and I think that's as close as we've been to doing it this year," Smith said. "It feels good to get the lead, then keep pushing and kind of put them out of their misery a little bit there."
Aston-Reese made it 4-1 at 3:16 of the third period when he put in his own rebound for his first goal since he was acquired in a trade with the Pittsburgh Penguins on March 21. The goal prevented Smith from getting his first shutout of the season.
"(Ducks forward) Gerry (Mayhew) stepped on my stick before going out for the third, and my tape job got cut in half," Aston-Reese said. "I was actually trying to go high glove and the puck just went five-hole. I can thank Gerry for that one."
Kulak, who was acquired in a trade with the Montreal Canadiens on March 21, made it 5-1 at 12:13 when his shot trickled between Gibson's pads.
Draisaitl sat on the bench the final few minutes of the first period and then limped to the locker room after appearing to injure himself while hitting Trevor Zegras behind the Anaheim net. He returned for the second period and had an assist on Kulak's goal.
He then scored his 50th goal with 3:58 left in the third to make it 6-1.
"Obviously I'm proud. I'm very happy about it, no question," Draisaitl said. "It also shows you how great my teammates are, right? They're the ones that put me in these situations. They're the ones that get me the puck in the right moments. We have such a selfless group out there, it's just fun to be a part of."