Phoenix defenseman Zbynek Michalek left after five shifts in the first period with a lower-body injury.
The Blackhawks jumped out to a 2-0 lead in the opening 6:22, but the Coyotes came back to tie it 2-all after the first period.
Saad opened the scoring 2:37 in when he popped in a rebound with Smith down on the ice and a scrum in the crease.
Sharp made it 2-0 at 6:22 with a power-play goal, on a rising shot fired from the top of the slot and through a screen.
The 23-year-old Stone cut it to 2-1 just 41 seconds later when his shot from the right point deflected off Pirri's stick and past Crawford.
Doan's power-play goal, chipped in from the right side of the net with 5:56 left in the first, tied it at 2. Keith Yandle's shot from the point missed the net, caromed off the back boards and straight to Doan.
Hossa put Chicago back ahead 3-2 at 5:05 of the second when he drove to the net unchecked and scored on a rebound of his own shot from left wing.
Korpikoski and Stone then scored 2:11 apart late in the second to put Phoenix ahead for the first time, 4-3.
From the edge of the crease, Korpikoski wrapped in a rebound of Vrbata's shot with 5:05 left in the period to knot it at 3. Stone's second goal, on a high drive from the top of the left circle, sailed past Crawford on the stick side and put the Coyotes in front.
After Pirri scored to tie it at 4, the Blackhawks took control and outshot the Coyotes 17-6 in the third. Smith stopped Hossa from point-blank range with a minute left in regulation.
Chicago dominated the overtime and outshot Phoenix 3-0.
NOTES: After the game, the Blackhawks announced they had reacquired forward Kris Versteeg, a member of their 2010 Stanley Cup championship team, from Florida as part of trade with the Panthers. ... The Blackhawks recalled 20-year-old forward Alex Broadhurst from Rockford of the AHL and placed C Michael Handzus on injured reserve retroactive to Oct. 25. Handzus has missed the last eight games with an upper-body injury. Broadhurst, from the Chicago suburb of New Lenox, Ill., didn't play Thursday. ... Chicago D Michal Rozsival was scratched. He was hit in the face with a puck on Sunday. ... Phoenix assigned forward Chris Brown to Portland of the American Hockey League. He had appeared in just four games.