Smith stopped 13 shots during a busy second period and all 11 Red Wings tries in the final frame, improving to 20-14-7 on the season.
Hanzal's tally 6:55 into the second period put the Coyotes ahead 2-0 and he added an empty-netter as Phoenix won for the third time in four contests.
Boyd Gordon also scored in the victory.
Campus cop fatally shoots Texas student during traffic stop
N.J. man wakes up from 10-hour sleep with knife in back