Mike Santorelli scored for the Canucks in the opening round of the shootout and Patrick Sharp came through for Chicago in the third round to keep the Blackhawks' hopes alive.
There was no further scoring until Kesler, the second shooter in the eighth round, put one past Antti Raanta.
Chicago lost in overtime for the sixth time this season, tying the Blackhawks for the lead in that department in the Western Conference.
Rookie Eddie Lack made 24 saves in regulation and overtime and stopped 7-of-8 in the shootout to get the win. Raanta was credited with stopping 22 shots.