The Blackhawks had lost four of their previous five games, but Patrick Kane scored twice in the third to finish off a dominating performance.
Kane gave Chicago a 3-0 lead with a power-play goal 4:15 into the third, after which Jordan Eberle ended Crawford's shutout bid with 3:40 remaining. Kane added an empty-net goal with 43 seconds to play.
Chicago won in Edmonton for sixth straight time.
Devan Dubnyk gave up three goals on 25 shots for the Oilers, who have lost 10 of their last 12. Edmonton has not won back-to-back games in more than two months.