Boedker, who had an assist in regulation, beat Corey Crawford from a daunting angle along the left goal line with 6:45 left in OT for his first career playoff goal, and gave the Coyotes a 2-1 lead in the best-of-seven series.
Crawford had 31 saves and shut the Coyotes out through the first two periods.
Andrew Burnett staked Chicago to a 1-0 with a goal at 19:13 of the first period. Michael Frolik scored at 8:49 of the third period to push the Blackhawks ahead 2-1, but Whitney quickly tied the score at 9:21.
2014: The Year in Music [PHOTOS]