Gagner netted both of his goals during a four-goal first period that gave the Oiler as a 4-0 lead after 20 minutes.
The Blackhawks, however, responded by scoring three of the next four goals in the middle frame to pull to within 5-3 before Hall scored on a power play with 4 minutes to go in the second.
Hall and Ryan Whitney each finished with a goal and an assist.
Starting Oilers goalie Devan Dubnyk was pulled in the second period after allowing two goals on 13 shots. Yann Danis relieved, turning aside 21-of-24 shots the rest of the way.
Kane finished with two goals and an assist for the Blackhawks, who dropped a second straight following 24 consecutive games without a regulation loss.