Teuvo Teravainen and rookie Phillip Danault were credited with assists on Desjardins' goal, while Andrew Shaw and Erik Gustafsson had helpers on Kane's tally.
Kane's 22nd goal of the season was his third point of the night after he recorded assists on Duncan Keith's and Artem Anisimov's power play goals in the first period. Brent Seabrook was originally credited with the second goal, but replay showed Anisimov deflected the puck in.
Keith also assisted on Artemi Panarin's power play goal that gave the Hawks a 3-2 lead after a pair of Arizona goals by Shane Doan and Zbynek Michalek. Both Arizona goals were assisted by Oliver Ekman-Larsson.