Smith, who blanked Dallas on Saturday, held the Blackhawks off the board until Patrick Sharp scored in the waning moments of regulation.
"They played a perfect checking game and frustrated us," said Blackhawks coach Joel Quenneville. "It wasn't pretty."
A fluid attack put the Coyotes on top late in the opening period. Doan began play from the blue line, centering to Whitney, whose touch pass found Langkow for a one-time backhand.
Midway through the second, Mikkel Boedker dropped a pass to Doan, who fired a slap shot from the right point for a 2-0 advantage.
Just 1:12 into the final period, Brent Seabrook lost possession behind his own net. Vrbata capitalized, scooping the loose puck and beating Crawford with a backhand.
Minutes later, Martin Hanzal's pass from behind the net found a wide-open Whitney, who buried a snap shot for a 4-0 lead.
Sharp scored off a centering pass from Patrick Kane with under a minute remaining, denying Smith his 14th career shutout.
"I think sometimes you come back home and you want to put on too much of a show for the fans," said Kane.
The Coyotes improved to 7-3-1 on the road this season...This was the second of four meetings between the teams this season. The Blackhawks won the initial matchup, 5-2...Langkow had two assists in Saturday's win over Dallas after returning from an extended absence due to the death of his mother.