Bryan Bickell had his second goal 11:36 into overtime and Chicago beat Phoenix after scoring in the closing seconds of regulation for the second straight game.
Phoenix won the opener 3-2 in overtime after giving up a goal to Brent Seabrook with 14 seconds left in regulation. Sharp did it to the Coyotes with even less time in Game 2, redirecting a shot by Patrick Kane with 5.5 seconds left.
The Blackhawks pulled it out this time, with Bickell beating Mike Smith from between the circles after Viktor Stalberg kept a pass by Rostislav Klesla in Phoenix's zone.
Brian Bollig also scored for Chicago. Antoine Vermette had two goals and nearly had a third in overtime, and Raffi Torres also scored for the Coyotes.
Smith made some big saves after nearly being knocked unconscious by Chicago's Andrew Shaw in the second period, but couldn't come up with the two that mattered the most, preventing Phoenix from going up 2-0 for the eighth straight playoff series since moving to the desert in 1996.
Game 3 in the Western Conference series is Tuesday night in Chicago.