Toews scored both of his goals in the first period, giving the Blackhawks a 2-0 lead. Chicago, however, blew a 3-1 lead in the second period and had to win it in the tiebreaker.
As the first shooter in the tiebreaker, he put one past Ilya Bryzgalov and Corey Crawford stopped Phoenix shooters Scottie Upshall, Radim Vrbata and Kyle Turris to wrap up the Blackhawks' fourth straight win, which kept them in the thick of the tightly packed Western Conference playoff race.
Crawford turned aside 26-of-29 shots and Marian Hossa also scored for Chicago.
Adrian Aucoin, Keith Yandle and Martin Hanzal found the net for the Coyotes.
Bryzgalov, meanwhile, finished with 38 saves.